<PAGE>
 
                                                                    EXHIBIT 10.1

                             THIRTEENTH AMENDMENT
                                    TO THE
                          SECOND AMENDED AND RESTATED
                       AGREEMENT OF LIMITED PARTNERSHIP
                                      OF
                              WEEKS REALTY, L.P.



     THIS THIRTEENTH AMENDMENT TO THE SECOND AMENDED AND RESTATED AGREEMENT OF
LIMITED PARTNERSHIP OF WEEKS REALTY, L.P. (the "Amendment") is entered into as
of the 7th day of August, 1998, by and among WEEKS GP HOLDINGS, INC., a Georgia
corporation (the "General Partner"), WEEKS CORPORATION, a Georgia corporation
(the "Company"), and ACKERMAN & CO., a Georgia general partnership (the
"Contributor").

                                 RECITALS
                                 --------

     Weeks Realty, L.P. (the "Partnership") is a Georgia limited partnership.
The General Partner is the sole general partner of the Partnership and is a
wholly owned subsidiary of the Company.  The partnership agreement of the
Partnership is that certain Second Amended and Restated Agreement of Limited
Partnership of Weeks Realty, L.P., dated as of October 30, 1996,  as amended by
the First Amendment to the Partnership Agreement dated November 1, 1996, the
Second Amendment to the Partnership Agreement dated December 31, 1996, the Third
Amendment to the Partnership Agreement dated January 31, 1997, the Fourth
Amendment to the Partnership Agreement dated August 1, 1997, the Fifth Amendment
to the Partnership Agreement dated October 7, 1997, the Sixth Amendment to the
Partnership Agreement dated October 27, 1997 , the Seventh Amendment to the
Partnership Agreement dated as of December 30,1997 and effective as of August 1,
1997, the Eighth Amendment to the Partnership Agreement dated January 9, 1998,
the Ninth Amendment to the Partnership Agreement dated January 22, 1998, the
Tenth Amendment to the Partnership Agreement dated April 3, 1998, the Eleventh
Amendment to the Partnership Agreement dated May 26, 1998, and the Twelfth
Amendment to the Partnership Agreement dated June 3, 1998 (the "Partnership
Agreement").  Capitalized terms used herein without definition shall have the
meanings ascribed to them in the Partnership Agreement.

     Pursuant to the agreements and instruments listed or referred to on Exhibit
                                                                         -------
A hereto (the ("Transaction Documents"), and the transactions effected by the
-                                                                            
Transaction Documents, effective as of the date hereof the Contributor has
contributed, directly or indirectly, certain properties to the capital of the
Partnership.

     Pursuant to the Partnership Agreement (including, without limitation,
Section 9.3 and Section 15.7(b)(ii) thereof), the General Partner is authorized
(without the consent of any Limited

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Partner) to admit additional Limited Partners to the Partnership for such
Capital Contributions as are determined by the General Partner to be
appropriate, and to amend the Partnership Agreement to reflect such admissions.

     The General Partner wishes to amend the Partnership Agreement as set forth
herein to reflect the admission of the Contributor as a Limited Partner of the
Partnership, and the Contributor wishes to enter into this Amendment to
memorialize its agreement as to certain matters relating to its becoming a
Limited Partner of the Partnership.

                                 AGREEMENT
                                 ---------

     In consideration of the circumstances referred to in the Recitals, the
consummation of the transactions effected pursuant to the Transaction Documents,
the mutual covenants and agreements contained herein, and other good and
valuable consideration, the receipt, adequacy and sufficiency of which are
hereby acknowledged, the parties hereto, intending to be legally bound, hereby
agree as follows:

     1.  Admission.  The Contributor is hereby admitted to the Partnership as a
         ---------                                                             
Limited Partner, effective as of the date hereof, and hereby agrees to be bound
by the Partnership Agreement, including, but not limited to, the transfer
restrictions contained in Article IX thereof.

     2.  Capital Contributions.  The Contributor has agreed to have made, as of
         ---------------------                                                 
the date hereof, the Capital Contribution set forth on Exhibit B hereto.  The
                                                       ---------             
agreed to gross fair market values of any property other than money contributed
by the Contributor, which shall be such property's initial Gross Asset Value, is
shown on Exhibit B.
         --------- 

     3.  Initial Partnership Units; Rights.
         --------------------------------- 

          (a) The Partnership Units attributable to the Partnership Interest of
     the Contributor, effective upon its admission as a Limited Partner at the
     date hereof, is as set forth on Exhibit B hereto, and the Partnership
                                     ---------                            
     Agreement is hereby amended to reflect the Contributor having such
     Partnership Units.

          (b) The Partnership does hereby grant to the Contributor, and
     Contributor hereby accepts, the right, but not the obligation (herein such
     rights being sometimes referred to as the "Rights"), to require the
     Partnership to redeem all or a portion of the Partnership Units issued to
     it pursuant to the Transaction Documents, on the terms and subject to the
     conditions and restrictions contained in Exhibit D hereto.  The Rights are
                                              ---------                        
     governed solely by this Amendment and Exhibit D hereto, and the Contributor
                                           ---------                            
     shall not have any rights with respect to the "Rights" provided for in
     Section 11.1 and Exhibit B-1 to the Partnership Agreement.  The Rights
                      -----------                                          
     granted hereunder may be exercised by the Contributor, on the terms and
     subject to the conditions and restrictions contained in Exhibit D hereto,
                                                             ---------        
     upon delivery to the Partnership of a Conversion Exercise Notice, in the
     form of Schedule 1 attached to Exhibit D, which notice shall specify the
                                    ---------                                
     Partnership

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<PAGE>
 
     Units with respect to which the Rights are being exercised.  Once
     delivered, the Conversion Exercise Notice shall be irrevocable, subject to
     compliance by the General Partner and the Partnership with the terms of the
     Rights.

     4.  Restated Percentage Interests.  After giving effect to the admission of
         -----------------------------                                          
the Contributor as a Limited Partner at the date hereof, the Percentage Interest
of the Contributor has been reflected on Exhibit C hereto, and the Partnership
                                         ---------                            
Agreement is hereby amended accordingly.

     5.  INTENTIONALLY OMITTED.


     6.  Tax Considerations.  In the event that Contributor elects to receive
         ------------------                                                  
Units hereunder, the General Partner will agree for the benefit of Contributor
that during the five-year period commencing on the date hereof, the General
Partner shall agree that (i) in the event it elects to cause the Partnership to
sell or otherwise convey any of the properties contributed to the Partnership
pursuant to this Agreement (each, a "Contributed Property"), the General Partner
will endeavor to structure any such sale or conveyance of a Contributed Property
as a tax-deferred like-kind exchange under section 1031 of the Code to the
extent such sale or conveyance would result in the recognition of gain for
federal income tax purposes by the Contributor, and (ii) the General Partner
will endeavor not to pay down or otherwise reduce (other than through regularly
scheduled payments of principal and interest) the amount of nonrecourse
indebtedness to which a Contributed Property is subject, to the extent that such
reduction would cause the Contributor to recognize gain for federal income tax
purposes.  The foregoing sentence shall not apply to gain recognized by the
Contributor as a result of cash distributions made by the Partnership in the
ordinary course of its operations subsequent to any such reduction in
nonrecourse indebtedness.  Notwithstanding the foregoing, the General Partner
shall have the right to sell Contributed Properties in one or more transactions
taxable in whole or in part, or to pay down or refinance nonrecourse debt
secured by a Contributed Property, if the General Partner determines, in good
faith, that such action is in the best economic interest of the Partnership and
the Partners (without taking into account the tax consequences of such action on
the Contributor), and, in such event, the General Partner agrees to provide
reasonable advance notice to the Contributor of such actions and to cooperate
with the Contributor in avoiding, to the extent feasible, any substantial
adverse federal income tax consequences to the Contributor resulting from such
actions (including, for example, by allowing the Contributor to assume deficit
capital account responsibility or by facilitating guarantees of other
Partnership nonrecourse indebtedness by the Contributor).


     7.  Proration of Distributions.  Notwithstanding any contrary provision of
         --------------------------                                            
the Partnership Agreement, including, without limitation, Section 6.2 thereof,
the Contributor agrees that the distribution of Net Operating Cash Flow made for
the calendar quarter in which the Partnership Units are issued, by reason of
each Capital Contribution made pursuant to the Transaction Documents shall be
equal to the amount of Net Operating Cash Flow otherwise distributable with
respect to such Partnership Units under the terms of the Partnership

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Agreement, multiplied by a fraction, the numerator of which is the number of
calendar days beginning on the date of issuance of the Partnership Units and
ending on the last day of such calendar quarter and the denominator of which is
the total number of days in the calendar quarter in which the Partnership Units
are issued.

     8.  Representations and Warranties.
         ------------------------------ 

          (a) Contributor's Representations.  The Contributor hereby reaffirms
              -----------------------------                                   
     and makes to each of the Partnership and the General Partner those
     representations and warranties made by Cobb Investors, Ltd. in the
     Contribution Agreement identified in Exhibit A attached hereto.  In
                                          ---------                     
     addition, the Contributor hereby represents and warrants to the Partnership
     and the General Partner that (i) the Contributor is acquiring the
     Partnership Units for the Contributor's own account and not with a view to,
     or for sale in connection with, the "distribution," as such term is used in
     Section 2(11) of the Securities Act of 1933, as amended (the "Securities
     Act"), of any of the Partnership Units in violation of the Securities Act;
     (ii) the Contributor is an "accredited investor," as that term is defined
     in Rule 501(a) of Regulation D promulgated under the Securities Act; (iii)
     the Contributor understands that the Partnership Units have not been
     registered under the Securities Act by reason of a specific exemption from
     the registration provisions of the Securities Act which depends upon, among
     other things, the nature of the investment intent and the accuracy of the
     Contributor's representations as expressed herein; (iv) the Contributor has
     had an opportunity to discuss the Partnership's business, management and
     financial affairs with the Partnership's management and the opportunity to
     review the Partnership's financial records; (v) the Contributor understands
     and acknowledges that no public market now exists for any of the
     Partnership Units and that there can be no assurance that a public market
     will ever exist for the Partnership Units; and (vi) the Contributor has
     such knowledge and experience in financial and business matters, or has
     been adequately advised by the Contributor's financial representatives,
     that the Contributor is capable of evaluating the merits and risks of the
     purchase of the Partnership Units pursuant to this Agreement and of
     protecting the Contributor's interests in connection herewith.

          (b) No Liens.  The Contributor represents and warrants to the
              --------                                                 
     Partnership and the General Partner that at the date hereof none of the
     Partnership Units issued or issuable to the Contributor pursuant to the
     Transaction Documents, and none of the shares of Common Stock that may be
     acquired by the Contributor upon exercise of Rights, is subject to any
     Lien, other than the security interest created by paragraph 11 hereof.

          (c) Definition.  All of the representations, warranties, covenants and
              ----------                                                        
     agreements of the Contributor referred to in this paragraph 8 are referred
     to collectively as the "Representations and Warranties."

          (d) General Partner Representations.  The General Partner represents
              -------------------------------                                 
     and warrants to the Contributor as follows:

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               (i) Organization.  The General Partner is duly incorporated,
                   ------------                                            
          validly existing and in good standing under the laws of the State of
          Georgia.

               (ii) Due Authorization; Binding Agreement.  The execution,
                    ------------------------------------                 
          delivery and performance of this Amendment by the General Partner have
          been duly and validly authorized by all necessary action of the
          General Partner and the Partnership.  This Amendment has been duly
          executed and delivered by the General Partner and constitutes a legal,
          valid and binding obligation of the General Partner and the
          Partnership, enforceable against the General Partner and the
          Partnership in accordance with the terms hereof.

               (iii)  Consents and Approvals.  No consent, waiver, approval or
                      ----------------------                                  
          authorization of, or filing, registration or qualification with, or
          notice to, any governmental unit or any other Person is required to be
          made, obtained or given by the General Partner in connection with the
          execution, delivery and performance of this Amendment, other than
          consents, waivers, approvals or authorizations that have been obtained
          prior to the date hereof.

               (iv) Partnership Units.  The Partnership Units  issued pursuant
                    -----------------                                         
          to the Transaction Documents are duly authorized and, when issued in
          accordance with the Transaction Documents, will be duly issued, fully
          paid and nonassessable and will be unencumbered except for the
          security interest created by paragraph 11 hereof.

     9.  Survival of Representations and Warranties.  All of the Representations
         ------------------------------------------                             
and Warranties shall survive the consummation of the transactions contemplated
by the Transaction Documents; provided, however, that no claim for a breach of
any Representation or Warranty may be maintained by the Partnership, the Company
or the General Partner unless the Partnership, the Company or the General
Partner shall have delivered a written notice ("Notice of Breach") specifying
the details of such claimed breach to the respective Contributor or before the
first anniversary of the last issuance of Units pursuant to the Transaction
Documents (the "Survival Period").

     10.  Indemnification.
          --------------- 

          (a) The Contributor hereby agrees to indemnify and hold harmless the
     Partnership, the Company and the General Partner against and from all
     liabilities, demands, claims, actions or causes of action, assessments,
     losses, fines, penalties, costs, damages and expenses (including, without
     limitation, reasonable attorneys' and accountants' fees and expenses
     actually incurred) sustained or incurred by the Partnership, the Company or
     the General Partner as a result of or arising out of any inaccuracy in or
     breach of a Representation or Warranty.

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<PAGE>
 
          (b) The Partnership, the Company and the General Partner shall not be
     entitled to indemnification hereunder unless a Notice of Breach has been
     delivered by the Partnership, the Company or the General Partner to the
     Contributor.

          (c) If a claim for indemnification is asserted by the Partnership, the
     Company or the General Partner against the Contributor, the Contributor
     shall have the right, at its own expense, to participate in the defense of
     any claim, action or proceeding asserted against the Partnership, the
     Company or the General Partner that resulted in the claim for
     indemnification, and if such right is exercised, the parties shall
     cooperate in the defense of such action or proceeding.

          (d) Indemnification of the Partnership, the Company and the General
     Partner pursuant to this paragraph 10 shall be the exclusive remedy of the
     Partnership, the Company and the General Partner for any breach of any
     Representation or Warranty contained in this contained in this Agreement.
     Nothing contained herein shall limit any remedy the Partnership (or any
     affiliate of the Partnership including, without limitation, any affiliate
     of the Partnership as determined with respect to the voting or economic
     control held by or in the Partnership) may have under the Transaction
     Documents, including, without limitation, the remedy of specific
     performance for any failure by the Contributor to contribute the property
     or otherwise limit any remedy the Partnership, the Company or the General
     Partner may have for any commission of fraud made by the Contributor.

     11.  Security and Remedies.
          --------------------- 

          (a) The Contributor hereby grants to the Partnership a lien upon and a
     continuing security interest in the Partnership Units issued to it pursuant
     to the Transaction Documents and the shares of Common Stock acquired by it
     upon exercise of Rights with respect to such Partnership Units (the
     "Collateral"), which shall be security for the indemnification obligations
     of the Contributor under paragraph 10 hereof.  Except as otherwise provided
     in this Amendment, the indemnification obligations of the Contributor
     hereunder with respect to breaches of Representations and Warranties shall
     be payable out of the Contributor's entire Collateral; provided, however,
     that the Contributor may satisfy all or any part of such indemnification
     obligation of the Contributor in cash if the Contributor so elects.  Any
     Transfer by the Contributor of its Collateral shall be subject to the lien
     and security interest granted hereby.

          (b) In the event the General Partner asserts that the Contributor has
     an indemnification obligation to the Partnership, the Company or the
     General Partner under paragraph 10 hereof, the General Partner shall
     deliver written notice (the "Indemnification Notice") to the Contributor
     describing in reasonable detail the circumstances giving rise to such
     obligation and the amount thereof.  If, within thirty (30) days after the
     receipt of an Indemnification Notice, the Contributor delivers written
     notice to the General Partner indicating that the Contributor disputes the
     circumstances giving rise to or the amount of

                                       6
<PAGE>
 
     such claimed indemnification obligation, the General Partner may submit
     such matter for binding arbitration in accordance with the provisions of
     Article XIV of the Partnership Agreement by delivering a Demand Notice to
     the Contributor pursuant to such Article XIV.  If, after receiving timely
     notice of a dispute hereunder from the Contributor, the General Partner
     fails to so submit the matter for arbitration within twenty (20) days after
     receipt of such notice from the Contributor, then the Contributor shall be
     relieved of the claimed indemnification obligation described in the
     Indemnification Notice.  In the event the Contributor (i) receives an
     Indemnification Notice and fail to timely deliver notice to the General
     Partner of its dispute as to the indemnification obligation and fails to
     make payment within thirty (30) days after delivery of an Indemnification
     Notice or (ii) has an indemnification obligation to the Partnership or the
     General Partner under paragraph 10 hereof as determined pursuant to Article
     XIV of the Partnership Agreement, and does not satisfy such obligation
     within ten (10) days after the decision rendered in the arbitration, then,
     in either event, the Partnership shall have any and all remedies of a
     secured creditor under the Uniform Commercial Code, and, in addition
     thereto, at the election of the Partnership, the Partnership shall, to the
     extent permitted by law, be deemed, without the payment of any further
     consideration or the taking of any further action required by the
     Contributor, to have acquired from the Contributor such portion of the
     Collateral as shall be equal in value (based, in the case of Partnership
     Units, on the Current Per Share Market Price as computed as of the date
     immediately preceding such deemed acquisition of the number of shares of
     Common Stock for which such Partnership Units could be redeemed if the
     General Partner assumed the redemption obligation and elected to pay the
     Redemption Price (as defined in Exhibit D) in shares of Common Stock
                                     ---------                           
     (assuming the ownership limits in the Articles of Incorporation would not
     prohibit the issuance of any such shares of Common Stock to the
     Contributor), and, in the case of shares of Common Stock, on the Current
     Per Share Common Stock Price computed as of the date immediately preceding
     such deemed acquisition) to the amount recoverable from the Contributor
     under paragraph 10 hereof.  In the event the Partnership shall have
     acquired from the Contributor any Collateral pursuant to this paragraph 11,
     the General Partner shall deliver written notice to the Contributor within
     ten (10) days thereafter identifying the specific Collateral acquired and,
     if such Collateral consists of Partnership Units, the Percentage Interests
     of the Contributor following such acquisition.  Unless and until the
     Partnership shall have acquired from the Contributor any Collateral
     pursuant to this paragraph 11, the Contributor shall retain all rights with
     respect to the Collateral not expressly limited herein or in the
     Partnership Agreement, including, without limitation, rights to
     distributions provided for in the Partnership Agreement and rights to
     dividends on shares of Common Stock. The Contributor hereby agrees to take
     any and all actions and to execute and deliver any and all documents or
     instruments necessary to perfect the security interest created by this
     Amendment, including delivering the certificates representing the
     Partnership Units or shares of Common Stock to the General Partner.

          (c) On the first day immediately following the expiration of the
     Survival Period as defined in paragraph 9 hereof (or, if a Notice of Breach
     has been delivered to the Contributor prior to such date, then on the first
     day immediately following the

                                       7
<PAGE>
 
     resolution of such Notice of Breach) the Contributor will be relieved of
     the restrictions on transferability provided for by this Amendment (except
     that the transfer restrictions contained in the Partnership Agreement shall
     continue) and the security interest in the Collateral shall terminate
     without further action, and the Partnership, at the request of the
     Contributor, shall promptly execute and deliver any document or instrument
     reasonably requested by the Contributor to evidence such termination.

     12.  Recourse.  Notwithstanding anything contained in this Amendment or in
          --------                                                             
the Partnership Agreement to the contrary, the recourse of the General Partner,
the Company or the Partnership under paragraph 10 hereof with respect to
breaches of Representations and Warranties of the Contributor shall not be
limited to the Contributor's Collateral.

     13.  Restriction on Transfer.  In connection with the security interests
          -----------------------                                            
granted by the Contributor under paragraph 11 hereof, the Contributor agrees
that any shares of Common Stock and any portion of the Contributor's Partnership
Interests included in the Collateral shall not be Transferred without the
consent of the General Partner; provided, however, that the Contributor may
Transfer all or any portion of such shares of Common Stock or Partnership
Interests to an Affiliate of such person (so long as such Affiliate remains an
Affiliate of such person), subject to the prior security interest granted in
paragraph 11 hereof and to the restrictions contained in Article IX of the
Partnership Agreement. Upon exercise of the Rights with respect to any
Partnership Units included in the Contributor's Collateral, the Partnership, in
perfection of the security interest herein granted, shall retain the
certificate(s) representing the portion of the Common Stock issued upon such
exercise that is included in such Collateral.  If any portion of the Partnership
Interests of Contributor included in Contributor's Collateral is represented by
certificates, the Partnership shall retain such certificates in perfection of
the security interest herein granted.  On the first day immediately following
the expiration of the Survival Period as defined in paragraph 9 hereof (or, if a
Notice of Breach has been delivered to the Contributor prior to such date, then
on the first day immediately following the resolution of such Notice of Breach)
the Contributor will be relieved of the restrictions on transferability provided
for by this paragraph 13 without further action, and the Partnership, at the
request of the Contributor, shall promptly execute and deliver any document or
instrument reasonably requested by the Contributor to evidence such termination.

     14.  Miscellaneous.  This Amendment shall be governed by and construed in
          -------------                                                       
conformity with the laws of the State of Georgia.  For the purposes of the
notice provisions of the Partnership Agreement, the address of the Contributor
is as set forth on the signature page hereof.  Except as expressly amended
hereby, the Partnership Agreement shall remain in full force and effect.  This
Amendment and all the terms and provisions hereof shall be binding upon and
shall inure to the benefit of the parties, and their legal representatives,
heirs, successors and permitted assigns.

                                       8
<PAGE>
 
     IN WITNESS WHEREOF, the parties have executed and delivered this Amendment
as of the date first above written.


                         WEEKS GP HOLDINGS, INC., a Georgia
                         corporation, its Sole General Partner


                              By:  /s/ Thomas D. Senkbeil
                                   ----------------------
                                   Name:  Thomas D. Senkbeil

                                   Title:  Vice Chairman and
                                           Chief Investment Officer



                     Signatures continued on following page

                                       9
<PAGE>
 
                         CONTRIBUTOR:

                         ACKERMAN & CO., a Georgia general
                         Partnership

                         By:  Charles S. Ackerman & Co., Inc.,
                              a Georgia corporation, authorized
                              general partner


                              By:  /s/ Charles S. Ackerman
                                   -----------------------
                                   Charles S. Ackerman, President



                                  Address:   c/o Ackerman & Co.
                                             1040 Crown Pointe Parkway
                                             Suite 200
                                             Atlanta, Georgia  30338
                                             Attn:  Mr. Charles S. Ackerman



                                  SOLELY TO EVIDENCE ITS AGREEMENT TO ITS
                                  UNDERTAKINGS IN EXHIBIT D HERETO:
                                                  ---------        


                                  WEEKS CORPORATION


                                  By: /s/ Thomas D. Senkbeil
                                      ----------------------
                                      Name:  Thomas D. Senkbeil
                                      Title:  Vice Chairman and
                                              Chief Investment Officer

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