<PAGE>
 
                                                                     EXHIBIT 4.5

THIS WARRANT AND THE SECURITIES REPRESENTED HEREBY HAVE NOT BEEN REGISTERED
UNDER THE SECURITIES ACT OF 1933, AS AMENDED, NOR PURSUANT TO THE SECURITIES OR
"BLUE SKY" LAWS OF ANY STATE AND MAY NOT BE TRANSFERRED, SOLD, OR OTHERWISE
DISPOSED OF, EXCEPT IN ACCORDANCE WITH APPLICABLE "BLUE SKY" LAWS AND PURSUANT
TO (i) A REGISTRATION STATEMENT WITH RESPECT TO SUCH SECURITIES WHICH IS
EFFECTIVE UNDER SUCH ACT, (ii) RULE 144 OR RULE 144A UNDER SUCH ACT, OR (iii)
ANY OTHER EXEMPTION FROM REGISTRATION UNDER SUCH ACT RELATING TO SUCH ACT,
PROVIDED THAT, IF REQUESTED BY WEEKS CORPORATION, AN OPINION OF COUNSEL
REASONABLY SATISFACTORY IN FORM AND SUBSTANCE IS FURNISHED TO WEEKS CORPORATION
THAT AN EXEMPTION FROM THE REGISTRATION REQUIREMENTS OF SUCH ACT IS AVAILABLE.

No. W-1                                                         November 6, 1998


                           WARRANT FOR THE PURCHASE
                       OF (i) SHARES OF COMMON STOCK OR
                     (ii) SHARES OF 8% SERIES A CUMULATIVE
                         REDEEMABLE PREFERRED STOCK OF
                               WEEKS CORPORATION


     THIS CERTIFIES THAT AEW Targeted Securities Fund, L.P., a Delaware limited
partnership (the "Holder"), for value received and subject to the terms and
conditions set forth in this Warrant (the "Warrant"), is entitled to purchase at
any time prior to the Expiration Date (as defined herein) from Weeks
Corporation, a Georgia corporation (the "Company"), either (i) 1,046,729 duly
authorized, validly issued, fully paid and nonassessable shares of Common Stock,
par value $.01 per share (the "Common Stock"), at a purchase price of $33.4375
per share (the "Initial Common Stock Exercise Price") or (ii) 1,400,000 duly
authorized, validly issued, fully paid and nonassessable shares of 8% Series A
Cumulative Redeemable Preferred Stock, par value $.01 per share (the "Preferred
Stock"), at a purchase price equal to the Liquidation Preference per share of
the Preferred Stock (the "Initial Preferred Stock Exercise Price").

     This Warrant is originally issued in connection with the execution and
delivery of the Securities Purchase Agreement dated as of November 6, 1998 (the
"Securities Purchase Agreement") by and among the Company, the Operating
Partnership and the Holder. This Warrant evidences the right to purchase an
aggregate of 1,046,729 shares of Common Stock or 1,400,000 shares of Preferred
Stock, subject to adjustment as provided herein. Certain capitalized terms used
in this Warrant are defined in Section 12 hereof.
<PAGE>
 
1.   EXERCISE OR PUT OF WARRANT.

     1.1  Manner of Exercise or Put; Payment
          ----------------------------------

          1.1.1  Exercise.  This Warrant may be exercised by the Holder, in
whole but not in part, during normal business hours on any Business Day on or
prior to the Expiration Date, if any, by surrender of this Warrant to the
Company at its principal office identified in Section 11.2(a) hereof,
accompanied by a subscription in substantially the form attached to this Warrant
duly executed by the Holder and accompanied by payment as set forth below.

          (i)    If the Warrant is exercised for Common Stock, the subscription
                 shall be accompanied by payment of, at the option of the
                 Holder, either (i) cash in an amount equal to, or (ii) shares
                 of Common Stock with an aggregate Current Market Price equal
                 to, the product of (a) the number of shares of Common Stock for
                 which this Warrant may be exercised multiplied by (b) the
                 Common Stock Exercise Price.

          (ii)   If the Warrant is exercised for Preferred Stock, the
                 subscription shall be accompanied by payment of, at the option
                 of the Holder, either (i) cash in an amount equal to, or (ii)
                 the number of Series C Preferred Partnership Units with an
                 aggregate Liquidation Preference Amount (including accrued and
                 unpaid quarterly distributions plus interest thereon) equal to,
                 the product of (a) the number of shares of Preferred Stock for
                 which this Warrant may be exercised multiplied by (b) the
                 Preferred Stock Exercise Price.

The Holder shall thereupon be entitled to receive the number of duly authorized,
validly issued, fully paid and nonassessable shares of Common Stock or Preferred
Stock (or Other Securities) determined as provided in Sections 2 through 4
hereof.

          1.1.2  Put.  This Warrant may be put by the Holder to the Company, in
whole but not in part, during normal business hours on any Business Day on or
prior to the Expiration Date, if any (the "Put Date"), by surrender of this
Warrant to the Company at its principal office identified in Section 11.2(a)
hereof, accompanied by a put notice in substantially the form attached to this
Warrant duly executed by the Holder, and the Holder shall thereupon be entitled
to receive, at the option of the Company, either:

          (i)    a number of duly authorized, validly issued, fully paid and
                 nonassessable shares of Common Stock (or Other Securities)
                 equal to:

                                       2
<PAGE>
 
                 (a)  the remainder of:

                      (x)  the product of (aa) the number of shares of Common
                           Stock (or Other Securities) determined as provided in
                           Sections 2 through 4 hereof which the Holder would as
                           of the Put Date be entitled to receive upon exercise
                           of this Warrant multiplied by (bb) the Current Market
                           Price as of the Put Date of each such share of Common
                           Stock (or such Other Securities) so receivable upon
                           such exercise

                      minus

                      (y)  $35,000,000

                 divided by

                 (b)  the Current Market Price as of the Put Date of each such
                      share of Common Stock (or Other Securities); or

          (ii)   cash in an amount equal to the aggregate Current Market Price
                 as of the Put Date of the shares of Common Stock (or Other
                 Securities) that would have been received pursuant to
                 subsection (i) above.

For all purposes of this Warrant (other than this Section 1.1), any reference
herein to the exercise of this Warrant shall be deemed to include a reference to
the put of this Warrant to the Company and the receipt therefor of shares of
Common Stock (or Other Securities) or cash in accordance with the terms of this
Section 1.1.2.

     1.2  Expiration Date.  This Warrant shall have a perpetual term; provided,
          ---------------                                             -------- 
however, that this Warrant shall expire the earliest of (i) thirty (30) days
-------                                                                     
after the Operating Partnership has redeemed the Series C Preferred Partnership
Units pursuant to Section 5(a) or 5(b) of the Partnership Amendment; (ii) the
date on which the Holder exercises its Put Right (as defined in the Partnership
Amendment); or (iii) the Merger Date (as defined in the Partnership Amendment)
if the Operating Partnership redeems the Series C Preferred Partnership Units
pursuant to Section 5(c) of the Partnership Amendment (any such date hereinafter
referred to as the "Expiration Date").

     1.3  Effectiveness of Exercise.  The exercise of this Warrant shall be
          -------------------------                                        
deemed to have been effected immediately prior to the close of business on the
Business Day on which this Warrant shall have been surrendered to the Company as
provided in Section 1.1 hereof, and at such time the Person or Persons in whose
name or names any certificate or certificates for

                                       3
<PAGE>
 
shares of Common Stock or Preferred Stock (or Other Securities) shall be
issuable upon such exercise as provided in Section 1.4 hereof shall be deemed to
have become the holder or holders of record thereof.

     1.4  Delivery of Stock Certificates and Cash.  As soon as practicable after
          ---------------------------------------                               
the exercise of this Warrant, and in any event within five (5) Business Days
thereafter, the Company will deliver to the Holder any cash to be paid to the
Holder pursuant to Section 1.1 hereof and, at its expense (including the payment
by it of any applicable issue taxes), will cause to be issued in the name of and
delivered to the Holder or, subject to Section 8 hereof, as the Holder (upon
payment by the Holder of any applicable transfer taxes) may direct, a
certificate or certificates for the number of duly authorized, validly issued,
fully paid and nonassessable shares of Common Stock or Preferred Stock (or Other
Securities) to which the Holder shall be entitled upon such exercise plus, in
lieu of any fractional share to which the Holder would otherwise be entitled,
cash in an amount equal to the same fraction of the Current Market Price per
share on the Business Day next preceding the date of such exercise.

     1.5  Company to Reaffirm Obligations.  The Company will, at the time of the
          -------------------------------                                       
exercise of this Warrant and upon the request of the Holder, acknowledge in
writing its continuing obligation to afford to the Holder all rights (including
without limitation the rights to registration, pursuant to the Registration
Rights Agreement referred to in Section 7 hereof, of the shares of Common Stock
or Preferred Stock (or Other Securities) issued upon such exercise) to which the
Holder shall continue to be entitled after such exercise in accordance with the
terms of this Warrant; provided, however, that if the Holder shall fail to make
                       --------  -------                                       
any such request, such failure shall not affect the continuing obligation of the
Company to afford such rights to the Holder.

2.   ADJUSTMENT OF STOCK ISSUABLE UPON EXERCISE

     2.1  General; Number of Shares; Exercise Price.
          ----------------------------------------- 

          2.1.1  Common Stock.  The number of shares of Common Stock which the
Holder shall be entitled to receive upon the exercise hereof shall be the number
of shares of Common Stock originally issuable upon the exercise of this Warrant
as adjusted, from time to time, pursuant to this Section 2. The aggregate
exercise price shall be determined by multiplying such number by the Common
Stock Exercise Price in effect on the date of such exercise. The "Common Stock
Exercise Price," which shall initially be the Initial Common Stock Exercise
Price, shall be adjusted and readjusted from time to time as provided in this
Section 2 and, as so adjusted and readjusted, shall remain in effect until a
further adjustment or readjustment thereof is required by this Section 2.

                                       4
<PAGE>
 
          2.1.2  Preferred Stock.  The number of shares of Preferred Stock which
the Holder shall be entitled to receive upon the exercise hereof shall be the
number of shares of Preferred Stock originally issuable upon the exercise of
this Warrant as adjusted, from time to time, pursuant to this Section 2. The
aggregate exercise price shall be determined by multiplying such number by the
Preferred Stock Exercise Price in effect on the date of such exercise. The
"Preferred Stock Exercise Price" which shall initially be the Initial Preferred
Stock Exercise Price, shall be adjusted and readjusted from time to time as
provided in this Section 2 and, as so adjusted and readjusted, shall remain in
effect until a further adjustment or readjustment thereof is required by this
Section 2.

     2.2  Adjustments for Dividends and Distributions.
          ------------------------------------------- 

          In case the Company at any time or from time to time after the date
hereof shall declare, order, pay or make a dividend or other distribution
(including without limitation any distribution of cash, other or additional
stock or other securities or property or the right to purchase any such
securities or property, by way of dividend or spin-off, reclassification,
recapitalization or similar corporate rearrangement or otherwise (except for
distributions in Common Stock)) on the Common Stock such that the aggregate
dividends and distributions per share paid on the Common Stock over the prior
twelve (12) month period exceed $2,675 per share (the "Dividend Cap") (the fair
market value of any non-cash distributions having been established in good faith
by the Board of Directors of the Company), then:

          (i)    in the case of a distribution in cash, the Common Stock
                 Exercise Price shall be reduced (without duplication) by an
                 amount equal to the per share amount of the cash dividend that
                 exceeds the Dividend Cap per share; and

          (ii)   in the case of any other distribution, the Company shall
                 provide the Holder with ten (10) Business Days' prior written
                 notice of such distribution and make appropriate provisions to
                 insure that the Holder shall thereafter have the right to
                 receive (without duplication), upon exercise of this Warrant,
                 in addition to the cash, Common Stock or Preferred Stock
                 immediately theretofore acquirable and recoverable upon
                 exercise of this Warrant, either, at the option of the Holder,
                 (a) such stock or other securities, property or rights as would
                 have been receivable by the Holder had this Warrant been
                 exercised prior to the time the Company took a record of
                 holders of Common Stock for purposes of entitling them to
                 receive such dividend or distribution, or (b) an amount of cash
                 equal to the fair market value of the property described in
                 clause (a) as of the date of such distribution, as determined
                 in good faith by the Board of Directors of the Company.

                                       5
<PAGE>
 
     The adjustment provided for in this Section 2.2 shall under no
circumstances reduce the Common Stock Exercise Price payable in connection with
any exercise of this Warrant below the par value per share issuable upon such
exercise.

     2.3  Adjustments for Subdivision or Combination.  If the Company at any
          ------------------------------------------                        
time or from time to time subdivides (by any stock split, stock dividend,
recapitalization or otherwise) its outstanding shares of Common Stock or
Preferred Stock into a greater number of shares or combines (by reverse stock
split or otherwise) its outstanding shares of Common Stock or Preferred Stock
into a lesser number of shares, immediately after the occurrence of such
subdivision or combination, the number of shares of Common Stock or Preferred
Stock, as applicable, for which this Warrant is exercisable shall be the number
of shares of Common Stock or Preferred Stock, as applicable, which a record
holder of the same number of shares of Common Stock or Preferred Stock, as
applicable, for which this Warrant is exercisable immediately prior to such
event would own or be entitled to receive in respect of such shares upon the
happening of such event. In the event an adjustment is made to the number of
shares of Common Stock or Preferred Stock for which this Warrant is exercisable,
(a) the Common Stock Exercise Price or the Preferred Stock Exercise Price, as
applicable, and, (b) in the case of an adjustment to the number of shares of
Common Stock for which this Warrant is exercisable, the Dividend Cap, shall be
adjusted by multiplying (i) each of the current Common Stock Exercise Price,
Preferred Exercise Price or Dividend Cap, as applicable, by (ii) a fraction
where the numerator is (y) the number of shares of Common Stock or Preferred
Stock, as applicable, for which this Warrant was exercisable immediately prior
to such adjustment over (z) the number of shares of Common Stock or Preferred
Stock, as applicable, for which this Warrant was exercisable immediately
following such adjustment.

     2.4  Adjustments for Consolidation, Merger, Sale of Assets, Etc.  In case
          -----------------------------------------------------------         
the Company after the date hereof (a) shall consolidate with or merge into any
other Person and shall not be the continuing or surviving corporation of such
consolidation or merger, or (b) shall permit any other Person to consolidate
with or merge into the Company and the Company shall be the continuing or
surviving Person but, in connection with such consolidation or merger, the
Common Stock, Preferred Stock or Other Securities shall be changed into or
exchanged for stock or other securities of any other Person or cash or any other
property, or (c) shall transfer all or substantially all of its properties or
assets to any other Person, or (d) shall effect a capital reorganization or
reclassification of the Common Stock, Preferred Stock or Other Securities, then,
and in the case of each such transaction, proper provision shall be made so
that, upon the basis and the terms and in the manner provided in this Warrant,
the Holder, upon the exercise hereof at any time after the consummation of such
transaction, shall be entitled to receive (at the aggregate Common Stock
Exercise Price or Preferred Stock Exercise Price, as applicable, in effect at
the time of such consummation for all Common Stock, Preferred Stock or Other
Securities issuable upon such exercise immediately prior to such consummation),
in lieu of the Common Stock, Preferred Stock or Other Securities 

                                       6
<PAGE>
 
issuable upon the exercise prior to such consummation, the greatest amount of
securities, cash or other property to which the Holder would actually have been
entitled as a shareholder upon such consummation if the Holder had exercised the
rights represented by this Warrant immediately prior thereto, subject to
adjustments (subsequent to such consummation) as nearly equivalent as possible
to the adjustments provided for in Section 2 hereof; provided, however, that if
                                                     --------  -------     
a purchase, tender or exchange offer shall have been made to and accepted by the
holders of more than fifty percent (50%) of the outstanding shares of Common
Stock, and if the Holder so designates in a notice given to the Company on or
before the date immediately preceding the date of the consummation of such
transaction, the Holder shall be entitled to receive upon such exercise the
greatest amount of securities, cash or other property to which the Holder would
actually have been entitled as a shareholder if the Holder had exercised such
Warrants prior to the expiration of such purchase, tender or exchange offer and
accepted such offer, subject to adjustments (from and after the consummation of
such purchase, tender or exchange offer) as nearly equivalent as possible to the
adjustments provided for in Section 2 hereof.

     2.5  Assumption of Obligations.  Notwithstanding anything contained in this
          -------------------------                                             
Warrant to the contrary, the Company will not effect any of the transactions
described in clauses (a) through (d) of Section 2.4 hereof unless, prior to the
consummation thereof, each person (other than the Company) which may be required
to deliver any stock, securities, cash or property upon the exercise of this
Warrant as provided herein shall by written instrument delivered to, and
reasonably satisfactory to, the Holder, assume (a) the obligations of the
Company under this Warrant (and if the Company shall survive the consummation of
such transaction, such assumption shall be in addition to, and shall not release
the Company from, any continuing obligations of the Company under this Warrant),
(b) the obligations of the Company under the Registration Rights Agreement and
(c) the obligation to deliver to the Holder such shares of stock, securities,
cash or property as, in accordance with the provisions of Section 2.4, the
Holder may be entitled to receive, and such Person shall have similarly
delivered to the Holder an opinion of counsel for such Person, which counsel
shall be reasonably satisfactory to the Holder, stating that this Warrant shall
thereafter continue in full force and effect and the terms hereof (including
without limitation all of the provisions of this Section 2) shall be applicable
to the stock, securities, cash or property which such Person may deliver upon
any exercise of this Warrant or the exercise of any rights pursuant hereto.

3.   OTHER DILUTIVE EVENTS.  In case any event shall occur as to which the
provisions of Section 2 hereof are not strictly applicable but the failure to
make any adjustment would not, in the opinion of the Holder, fairly protect the
purchase rights represented by this Warrant in accordance with the essential
intent and principles of such Section, then, in each such case, at the request
of the Holder, the Company shall appoint a firm of independent investment
bankers of recognized national standing (which shall be completely independent
of the Company and shall be satisfactory to the Holder), which shall give their
opinion upon the

                                       7
<PAGE>
 
adjustment, if any, on a basis consistent with the essential intent and
principles established in Section 2 hereof, necessary to preserve, without
dilution, the purchase rights represented by this Warrant. Upon receipt of such
opinion, the Company will promptly mail a copy thereof to the Holder and shall
make the adjustments described therein.

4.   NO DILUTION OR IMPAIRMENT.  The Company will not, by amendment of its
articles of incorporation or through any consolidation, merger, reorganization,
transfer of assets, dissolution, issue or sale of securities or any other
voluntary action, avoid or seek to avoid the observance or performance of any of
the terms of this Warrant, but will at all times in good faith assist in the
carrying out of all such terms and in the taking of all such action as may be
necessary or appropriate in order to protect the rights of the holder of this
Warrant against dilution or other impairment. Without limiting the generality of
the foregoing, the Company (a) will not permit the par value of any shares of
stock receivable upon the exercise of this Warrant to exceed the amount payable
therefor upon such exercise, (b) will take all such action as may be necessary
or appropriate in order that the Company may validly and legally issue fully
paid and nonassessable shares of stock on the exercise of the Warrants from time
to time outstanding, and (c) will not take any action which results in any
adjustment of the Common Stock Exercise Price or the Preferred Stock Exercise
Price if the total number of shares of Common Stock, Preferred Stock (or Other
Securities) issuable after the action upon the exercise of all of the Warrants
would exceed the total number of shares of Common Stock, Preferred Stock (or
Other Securities) then authorized by the Company's articles of incorporation and
available for the purpose of issue upon such exercise.

5.   ACCOUNTANTS' REPORT AS TO ADJUSTMENTS.  In each case of any adjustment or
readjustment in the shares of Common Stock or Preferred Stock (or Other
Securities) issuable upon the exercise of this Warrant, the Company will
promptly compute such adjustment or readjustment in accordance with the terms of
this Warrant. In the event of a dispute in connection with such adjustment, the
Company at its own expense will cause independent certified public accountants
of recognized national standing (which may be the regular auditors of the
Company) selected by the Company to verify such computation (other than any
computation of the fair value of property as determined in good faith by the
Board of Directors of the Company) and prepare a report setting forth such
adjustment or readjustment and showing in reasonable detail the method of
calculation thereof and the facts upon which such adjustment or re-adjustment is
based. The Company will forthwith mail a copy of each such report to the Holder
and will, upon the written request at any time of the Holder, furnish to the
Holder a like report setting forth the Common Stock Exercise Price and the
Preferred Stock Exercise Price at the time in effect and showing in reasonable
detail how it was calculated. The Company will also keep copies of all such
reports at its office maintained pursuant to Section 11.2(a) hereof and will
cause the same to be available for inspection at such office during normal
business hours by the Holder or any prospective purchaser of a Warrant
designated by the holder thereof.

                                       8
<PAGE>
 
6.   NOTICES OF CORPORATE ACTION.  In the event of

          (a)  any taking by the Company of a record of the holders of any class
     of securities for the purpose of determining the holders thereof who are
     entitled to receive any dividend or other distribution (other than the
     Company's regular quarterly cash dividends provided that any such dividend
     does not cause the Company's aggregate distributions for the prior twelve
     (12) month period to exceed the Dividend Cap), or any right to subscribe
     for, purchase or otherwise acquire any shares of stock of any class or any
     other securities or property, or to receive any other right, or

          (b)  any capital reorganization of the Company, any reclassification
     or recapitalization of the capital stock of the Company or any
     consolidation or merger involving the Company and any other Person or any
     transfer of all or substantially all the assets of the Company to any other
     Person, or

          (c)  any voluntary or involuntary dissolution, liquidation or winding-
     up of the Company,

the Company will mail to the Holder a notice specifying (i) the date or expected
date on which any such record is to be taken for the purpose of such dividend,
distribution or right, and the amount and character of such dividend,
distribution or right and (ii) the date or the date on which any such
reorganization, reclassification, recapitalization, consolidation, merger,
transfer, dissolution, liquidation or winding-up is to take place, the time, if
any such time is to be fixed, as of which the holders of record of Common Stock
or Preferred Stock (or Other Securities) shall be entitled to exchange their
shares of Common Stock or Preferred Stock (or Other Securities) for the
securities or other property deliverable upon such reorganization,
reclassification, recapitalization, consolidation, merger, transfer,
dissolution, liquidation or winding-up and a description in reasonable detail of
the transaction. Such notice shall be mailed at least thirty (30) days prior to
the date therein specified.

7.   REGISTRATION OF COMMON STOCK OR PREFERRED STOCK.  The shares of Common
Stock and Preferred Stock (and Other Securities) issuable upon exercise of this
Warrant shall constitute Registrable Securities (as such term is defined in the
Registration Rights Agreement). The Holder of this Warrant shall be entitled to
all of the benefits afforded to a holder of any such Registrable Securities
under the Registration Rights Agreement and the Holder, by its acceptance of
this Warrant, agrees to be bound by and agrees to the terms and conditions of
the Registration Rights Agreement applicable to the Holder as a holder of such
Registrable Securities. If requested by the Company, the Holder shall execute a
counterpart signature page to the Registration Rights Agreement.

                                       9
<PAGE>
 
8.   RESTRICTIONS ON TRANSFER.

     8.1  Not Divisible.  This Warrant may not be divided and may only be
          -------------                                                  
transferred in whole.

     8.2  Restrictive Legends.  Except as otherwise permitted by this Section 8,
          -------------------                                                   
each certificate for Common Stock or Preferred Stock (or Other Securities)
issued upon the exercise of this Warrant, each certificate issued upon the
direct or indirect transfer of any such Common Stock or Preferred Stock (or
Other Securities), this Warrant originally issued pursuant to the Securities
Purchase Agreement and each Warrant issued upon direct or indirect transfer or
in substitution for any Warrant pursuant to Section 11 hereof shall be
transferable only upon satisfaction of the conditions specified in Section 6 of
the Securities Purchase Agreement and in this Section 8 and shall be stamped or
otherwise imprinted with legends in substantially the form required by Section
6.1 of the Securities Purchase Agreement.

     Notwithstanding any other provision of this Section 8 or of the Securities
Purchase Agreement, no opinion of counsel shall be necessary for a transfer of
Restricted Securities by the holder thereof to a subsidiary, shareholder,
partner or other affiliate of such holder, if the transferee agrees in writing
to be subject to the terms hereof to the same extent as if such transferee were
the original Holder of this Warrant.

9.   AVAILABILITY OF INFORMATION.  If the Company shall have filed a
registration statement pursuant to the requirements of Section 12 of the
Exchange Act or a registration statement pursuant to the requirements of the
Securities Act, the Company will comply with the reporting requirements of
Sections 13 and 15(d) of the Exchange Act and will comply with all other public
information reporting requirements of the Commission (including Rule 144 and
144A promulgated by the Commission under the Securities Act) from time to time
in effect and relating to the availability of an exemption from the Securities
Act for the sale of any Restricted Securities.  The Company will also cooperate
with each holder of any Restricted Securities in supplying such information as
may be necessary for such holder to complete and file any information reporting
forms presently or hereafter required by the Commission as a condition to the
availability of an exemption from the Securities Act for the sale of any
Restricted Securities.  The Company will furnish to the Holder of this Warrant,
promptly upon their becoming available, copies of all financial statements,
reports, notices and proxy statements sent or made available generally by the
Company to its stockholders, and copies of all regular and periodic reports and
all registration statements and prospectuses filed by the Company with any
securities exchange or with the Commission.

10.  RESERVATION OF STOCK.  The Company will at all times reserve and keep
available, solely for issuance and delivery upon exercise of this Warrant, the
number of shares of Common Stock and Preferred Stock (or Other Securities) 
from time to time issuable upon exercise of this Warrant. All shares of Common
Stock and Preferred Stock (or Other Securities) 

                                       10
<PAGE>
 
issuable upon exercise of this Warrant shall be duly authorized and, when issued
upon such exercise, shall be validly issued and, in the case of shares, fully
paid and nonassessable with no liability on the part of the holders thereof.

11.  OWNERSHIP, TRANSFER AND SUBSTITUTION OF WARRANTS.

     11.  Ownership of Warrants.  The Company may treat the person in whose name
          ---------------------                                                 
this Warrant is registered on the register kept at the office of the Company
maintained pursuant to Section 11.2(a) hereof as the owner and Holder thereof
for all purposes, notwithstanding any notice to the contrary.  This Warrant may
be exercised by a new Holder without a new Warrant first having been issued.

     11.  Office; Transfer and Exchange of Warrants:
          ----------------------------------------- 

          (a) Company will maintain an office in Norcross, Georgia where
     notices, presentations and demands in respect of this Warrant may be made
     upon it.  Such office shall be maintained at 4497 Park Drive, Norcross,
     Georgia  30093 until such time as the Company shall notify the holders of
     this Warrant of any change of location of such office.

          (b) The Company shall cause to be kept at its office maintained
     pursuant to Section 11.2(a) hereof a register for the registration and
     transfer of this Warrant.  The name and address of the Holder of this
     Warrant, the transfers thereof and the names and addresses of transferees
     of this Warrant shall be registered in such register.  The Person in whose
     name this Warrant shall be so registered shall be deemed and treated as the
     owner and Holder thereof for all purposes of this Warrant, and the Company
     shall not be affected by any notice or knowledge to the contrary.

          (c) Upon the surrender of this Warrant, properly endorsed, for
     registration of transfer or for exchange at the office of the Company
     maintained pursuant to Section 11.2(a) hereof, the Company at its expense
     will execute and deliver to or upon the order of the Holder thereof a new
     Warrant of like tenor, in the name of such Holder or as such Holder (upon
     payment by such holder of any applicable transfer taxes) may direct,
     calling in the aggregate on the face thereof for the number of shares of
     Common Stock or Preferred Stock called for on the face of the Warrant so
     surrendered.

     11.  Replacement Of Warrant.  Upon receipt of evidence reasonably
          ----------------------                                      
satisfactory to the Company of the loss, theft, destruction or mutilation of
this Warrant and, in the case of any such mutilation, upon surrender of such
Warrant for cancellation at the office of the Company maintained pursuant to
Section 11.2(a) hereof, the Company at its expense will execute and deliver, in
lieu thereof, a new Warrant of like tenor and dated the date hereof.  The Holder
shall provide such security or indemnity as the Company may require to hold the
Company and its agents harmless from such replacement of the Warrant.

                                       11
<PAGE>
 
12.  DEFINITIONS.

     Business Day.  Any day other than a Saturday or Sunday or a day on which
commercial banking institutions in Boston, Massachusetts, New York, New York or
Atlanta, Georgia are authorized by law to be closed.  Any reference to "days"
(unless Business Days are specified) shall mean calendar days.

     Commission.  The Securities and Exchange Commission or any other federal
agency at the time administering the Securities Act.

     Common Stock.  As defined in the introduction to this Warrant, such term to
include any stock into which such Common Stock shall have been changed or any
stock resulting from any reclassification of such Common Stock, and all other
stock of any class or classes (however designated) of the Company the holders of
which have the right, without limitation as to amount, either to all or to a
share of the balance of current dividends and liquidating dividends after the
payment of dividends and distributions on any shares entitled to preference.

     Common Stock Exercise Price.  As defined in Section 2.1.1.

     Company.  As defined in the introduction to this Warrant, such term to
include any corporation which shall succeed to or assume the obligations of the
Company hereunder in compliance with Section 2 hereof.

     Current Market Price.  With respect to the Common Stock, on any date
specified herein, the average of the Market Price during the period of the most
recent 10 consecutive trading days ending on such date.

     Exchange Act.  The Securities Exchange Act of 1934, or any similar federal
statute, and the rules and regulations of the Commission thereunder, all as the
same shall be in effect at the time.

     Expiration Date.  As defined in Section 1.2 hereof.

     Holder.  The original holder of this Warrant identified in the introduction
and any Person to whom this Warrant is transferred.

     Initial Common Stock Exercise Price.  As defined in the introduction to
this Warrant.

     Liquidation Preference.  The Liquidation Preference of the Company's Series
A Preferred Stock as set forth in the Company's Articles of Amendment relating
to the Preferred Stock.

                                       12
<PAGE>
 
     Liquidation Preference Amount.  As defined in the Partnership Amendment.

     Market Price. With respect to the Common Stock, on any date shall mean the
last sale price, regular way, or, in case no such sale takes place on such day,
the average of the closing bid and asked prices, regular way, in either case as
reported in the principal consolidated transaction reporting system with respect
to securities listed or admitted to trading on the New York Stock Exchange or,
if the Common Stock is not listed or admitted to trading on the New York Stock
Exchange, as reported in the principal consolidated transaction reporting system
with respect to securities listed on the principal national securities exchange
on which the Common Stock is listed or admitted to trading or, if the Common
Stock is not listed or admitted to trading on any national securities exchange,
the last quoted price, or if not so quoted, the average of the high bid and low
asked prices in the over-the-counter market, as reported by the NASD Automated
Quotation System or, if such system is no longer in use, the principal other
automated quotation system that may then be in use, or if the Common Stock is
not quoted by any such organization, the average of the closing bid and asked
prices as furnished by a professional market maker making a market in the Common
Stock that is selected by the Board of Directors of the Company, or, if there is
no such professional market maker, such amount as an independent investment
banking firm selected by the Board of Directors of the Company determines to be
the value of a share of Common Stock.

     NASD.  The National Association of Securities Dealers, Inc.

     Operating Partnership.  Weeks Realty, L.P., a Georgia limited partnership.

     Other Securities.  Any stock (other than Common Stock or Preferred Stock)
and other securities of the Company or any other Person which the Holder at any
time shall be entitled to receive, or shall have received, upon the exercise of
the Warrant, in lieu of or in addition to Common Stock or Preferred Stock, or
which at any time shall be issuable or shall have been issued in exchange for or
in replacement of Common Stock, Preferred Stock or Other Securities pursuant to
Section 3 hereof or otherwise.

     Partnership Agreement. The Second Amended and Restated Agreement of Limited
Partnership of the Operating Partnership, as amended.

     Partnership Amendment.  The Fourteenth Amendment to the Partnership
Agreement by and between the Operating Partnership and the Purchaser.

     Person.  A corporation, an association, a partnership, an organization, a
business, an individual, a government or political subdivision thereof or a
governmental agency.

                                       13
<PAGE>
 
     Preferred Stock.  As defined in the introduction to this Warrant, such term
to include any stock into which such Preferred Stock shall have been changed or
any stock resulting from any reclassification of such Preferred Stock.

     Preferred Stock Exercise Price.  As defined in the introduction to this
Warrant.

     Registration Rights Agreement.  The Registration Rights Agreement in the
form of Exhibit B to the Securities Purchase Agreement, as from time to time in
effect.

     Restricted Securities.  All of the following: (a) this Warrant which shall
bear the legend or legends referred to in Section 8 hereof, (b) any shares of
Common Stock or Preferred Stock (or Other Securities) which have been issued
upon the exercise of this Warrant and which are evidenced by a certificate or
certificates bearing the applicable legend or legends referred to in such
Section, (c) unless the context otherwise requires, any shares of Common Stock
or Preferred Stock (or Other Securities) which are at the time issuable upon the
exercise of this Warrant and which, when so issued, will be evidenced by a
certificate or certificates bearing the applicable legend or legends referred to
in such Section.

     Securities Act.  The Securities Act of 1933, or any similar federal
statute, and the rules and regulations of the Commission thereunder, all as the
same shall be in effect at the time.

     Securities Purchase Agreement.  As defined in the introduction to this
Warrant.

     Series C Preferred Partnership Units.  Series C Preferred Partnership Units
of the Operating Partnership.

13.  REMEDIES.  The Company stipulates that the remedies at law of the Holder in
the event of any default or threatened default by the Company in the performance
of or compliance with any of the terms of this Warrant are not and will not be
adequate and that, to the fullest extent permitted by law, such terms may be
specifically enforced by a decree for the specific performance of any agreement
contained herein or by an injunction against a violation of any of the terms
hereof or otherwise.

14.  NO LIABILITIES AS STOCKHOLDER.  Nothing contained in this Warrant shall be
construed as conferring upon the Holder any rights as a stockholder of the
Company or as imposing any obligation on the Holder to purchase any securities
or as imposing any liabilities on the Holder as a stockholder of the Company,
whether such obligation or liabilities are asserted by the Company or by
creditors of the Company.

15.  NOTICES.   Except as otherwise provided in this Warrant, notices and other
communications under this Warrant shall be in writing and shall be delivered, or
mailed by registered or certified mail, return receipt requested, or by a
nationally recognized overnight 

                                       14
<PAGE>
 
courier, postage prepaid, addressed, (a) if to the Holder, at the address set
forth in the register kept at the office of the Company maintained pursuant to
Section 11.2(a) hereof or such other address as the Holder shall have furnished
to the Company in writing, or (b) if to any other holder of any Securities, at
such address as such other holder shall have furnished to the Company in
writing, or, until any such other holder so furnishes to the Company an address,
then to and at the address of the last holder of such Securities who has
furnished an address to the Company, or (c) if to the Company, at its address
maintained pursuant to Section 11.2(a) hereof, to the attention of the
President, or at such other address, or to the attention of such other officer,
the Company shall have furnished to the Holder and each such other holder in
writing, with a copy to William B. Fryer, King & Spalding, 191 Peachtree Street,
Atlanta, Georgia 30303-1703. This Warrant and all other documents delivered in
connection with the transactions contemplated by the Securities Purchase
Agreement embody the entire agreement and understanding between the Holder and
the Company and supersedes all prior agreements and understandings relating to
the subject matter hereof.

16.  GOVERNING LAW.  This Warrant shall be construed and enforced in accordance
with and governed by the laws of the State of Georgia.

17.  AMENDMENTS.  This Warrant and any term hereof may be changed, waived,
discharged or terminated only by an instrument in writing signed by the party
against which enforcement of such change, waiver, discharge or termination is
sought.

18.  HEADINGS.  The Section headings in this Warrant are for purposes of
convenience only and shall not constitute a part hereof.

                              WEEKS CORPORATION


                              By:________________________
                                 Name:
                                 Title:

                                       15
<PAGE>
 
                              FORM OF SUBSCRIPTION
                              --------------------


Date:

Weeks Corporation
[address]

     The undersigned registered Holder of the within Warrant hereby irrevocably
exercises such Warrant for, and purchases thereunder, for _______ shares of
[COMMON STOCK/PREFERRED STOCK] and herewith makes payment of [CASH EQUAL TO OR
_________ SHARES OF COMMON STOCK/PREFERRED UNITS WITH A VALUE OF] $__________
therefor, and requests that a certificate for such shares be issued in the name
of the undersigned and be delivered to the undersigned at the address stated
below.



                                      BY:  AEW TSF, LLC., its General Partner


                                           By:______________________
                                              Name:
                                              Title:


                                      Address:  c/o AEW Capital Management, L.P.
                                                225 Franklin Street
                                                Boston, MA  02110

                                       16
<PAGE>
 
                               FORM OF PUT NOTICE
                               ------------------


Date:

Weeks Corporation
[ADDRESS]

     The undersigned registered Holder of the within Warrant hereby irrevocably
puts to the Company such Warrant with respect to, at the option of the Company,
either (i) _______ shares of Common Stock or (ii) cash in the amount of
$__________, which such holder would be entitled to receive upon the put hereof,
and, if the Company elects to issue shares of Common Stock in respect of such
put, the undersigned requests that a certificate for such shares be issued in
the name of the undersigned and be delivered to the undersigned at the address
stated below.



                         Signed:  AEW TARGETED SECURITIES FUND, L.P.

                                  By: AEW TSF, L.L.C., its General Partner

                                      By: AEW TSF, INC., its General Partner

                                          By:______________________
                                             Name:
                                             Title:

                                  Address: c/o AEW Capital Management, L.P.
                                           225 Franklin Street
                                           Boston, MA  02110

                                       17