<PAGE>
                                                                    EXHIBIT 10.6
 
                               TWELFTH AMENDMENT
                                    TO THE
                          SECOND AMENDED AND RESTATED
                       AGREEMENT OF LIMITED PARTNERSHIP
                                      OF
                              WEEKS REALTY, L.P.



     THIS TWELFTH AMENDMENT TO THE SECOND AMENDED AND RESTATED AGREEMENT OF
LIMITED PARTNERSHIP OF WEEKS REALTY, L.P. (the "Amendment") is entered into as
of the 3rd day of June 1998, by and among WEEKS GP HOLDINGS, INC., a Georgia
corporation (the "General Partner"), WEEKS CORPORATION, a Georgia corporation
(the "Company"), and THOMAS M. BECKMAN and THOMAS B. FOWLER, JR. (Beckman and
Fowler are collectively referred to hereafter as the "Contributors" and
"Contributor" shall hereafter mean any one of the Contributors).

                                   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, and the
Eleventh Amendment to the Partnership Agreement dated May 26,1998, (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 Contributors have
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 
<PAGE>
 
Limited 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 Contributors as Limited Partners of the
Partnership, and the Contributors wish to enter into this Amendment to
memorialize their agreement as to certain matters relating to their becoming
Limited Partners 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 Contributors are hereby admitted to the Partnership as
         ---------                                                             
Limited Partners, effective as of the date hereof, and each of the Contributors
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 Contributors are agreed to have made, as of
         ---------------------                                                  
the date hereof, the Capital Contributions set forth on Exhibit B hereto.  The
                                                        ---------             
agreed to gross fair market values of any property other than money contributed
by each of the Contributors, which shall be such property's initial Gross Asset
Value, are shown on Exhibit B.
                    --------- 

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

          (a) The Partnership Units attributable to the Partnership Interests of
     the Contributors, effective upon their admission as Limited Partners at the
     date hereof, are as set forth on Exhibit B hereto, and the Partnership
                                      ---------                            
     Agreement is hereby amended to reflect the Contributors' having such
     Partnership Units.

          (b) The Partnership does hereby grant to each of the Contributors, and
     each of them does hereby accept, 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
     them 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 none of the
                                           ---------                        
     Contributors shall 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 any one or more of the
     Contributors, on the terms and subject to the conditions and restrictions
     contained in Exhibit D hereto, upon delivery to the Partnership 
                  ---------
<PAGE>
 
     of a Conversion Exercise Notice, in the form of Schedule 1 attached to
     Exhibit D, which notice shall specify the Partnership 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 Contributors as Limited Partners at the date hereof, the Percentage
Interests of the Contributors have been reflected on Exhibit C hereto, and the
                                                     ---------                
Partnership Agreement is hereby amended accordingly.

     5.  Future Contributions.  The parties acknowledge that, pursuant to and
         --------------------                                                
subject to the terms and conditions of the Transaction Documents, the
Contributors may make additional Capital Contributions.  Concurrently with any
such additional Capital Contribution, the General Partner shall supplement this
Amendment by executing and attaching hereto supplements to Exhibits B and C
                                                           ----------------
(which shall be captioned "Exhibit B-1," "Exhibit B-2," "Exhibit C-1," "Exhibit
                           -----------    -----------    -----------    -------
C-2," and so on and shall identify the Capital Contribution to which each
---                                                                      
relates) that will, respectively, reflect (to the extent determinable at such
time) the Capital Contribution made by the Contributors at that time, the
initial Gross Asset Value of any property other than money included in such
Capital Contribution, the additional Partnership Units attributable to the
Partnership Interest associated with such Capital Contribution, and the
resulting restated Percentage Interests of all of the Partners.  Such
supplements shall be in accordance with the terms of the Transaction Documents.
The Partnership Agreement shall be deemed to be amended as reflected in each
such supplement to this Amendment.

     6.  Adjustments to Partnership Units. The parties acknowledge that the
         --------------------------------                                  
Transaction Documents provide for adjustments to the Partnership Units of the
Contributors in certain circumstances, and further provide that the
Contributors' Partnership Interests and Units, and the resulting restated
Percentage Interests of all of the Partners, may not be capable of determination
at the time a Capital Contribution is made after the date hereof.  At the times
of adjustment and final determination provided for in the Transaction Documents,
the General Partner shall supplement this Amendment by executing and attaching
hereto either additional supplements to Exhibits B and C (in the form described
                                        ----------------                       
above), or amended and restated versions of prior supplements to Exhibits B and
                                                                 --------------
C, as applicable.  Such supplements shall be in accordance with the terms of the
-                                                                               
Transaction Documents.  The Partnership Agreement shall be deemed to be amended
as reflected in each such supplement to this Amendment.

     7.  Proration of Distributions.  Notwithstanding any contrary provision of
         --------------------------                                            
the Partnership Agreement, including, without limitation, Section 6.2 thereof,
the Contributors agree 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 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 
<PAGE>
 
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) Contributors' Representations.  The Contributors, jointly and
              -----------------------------                                
     severally, hereby reaffirm and make to each of the Partnership and the
     General Partner those representations and warranties contained in the
     Contribution Agreement identified in Exhibit A attached hereto.  In
     addition, the Contributors, jointly and severally, hereby represent and
     warrant to the Partnership and the General Partner that (i) each such
     Contributor is acquiring the Partnership Units for such 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) each such Contributor is an
     "accredited investor," as that term is defined in Rule 501(a) of Regulation
     D promulgated under the Securities Act; (iii) each such 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 such Contributor's
     representations as expressed herein; (iv) each such 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) each such 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) each such Contributor has such
     knowledge and experience in financial and business matters, or has been
     adequately advised by such Contributor's financial representatives, that
     such Contributor is capable of evaluating the merits and risks of the
     purchase of the Partnership Units pursuant to this Agreement and of
     protecting such Contributor's interests in connection herewith.

          (b) No Liens.  The Contributors, jointly and severally, represent and
              --------                                                         
     warrant to the Partnership and the General Partner that at the date hereof
     none of the Partnership Units issued or issuable to the Contributors
     pursuant to the Transaction Documents, and none of the shares of Common
     Stock that may be acquired by the Contributors 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 each of the Contributors 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 each of the Contributors as follows:
<PAGE>
 
               (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 Contributors, jointly and severally, 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.
<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
     Contributors.

          (c) If a claim for indemnification is asserted by the Partnership, the
     Company or the General Partner against the Contributors, the Contributors
     shall have the right, at their 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 a 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) Each of the Contributors hereby grants to the Partnership a lien
     upon and a continuing security interest in the Partnership Units issued to
     each of them pursuant to the Transaction Documents and the shares of Common
     Stock acquired by each of them upon exercise of Rights with respect to such
     Partnership Units (the "Collateral"), which shall be security for the
     indemnification obligations of the Contributors under paragraph 10 hereof.
     Except as otherwise provided in this Amendment, the indemnification
     obligations of the Contributors hereunder with respect to breaches of
     Representations and Warranties shall be payable out of the Contributors
     entire Collateral; provided, however, that the Contributors may satisfy all
     or any part of such indemnification obligation of the Contributors in cash
     if the Contributors so elect.  Any Transfer by a 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 Contributors
     have 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 Contributors
     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 Contributors deliver written
     notice to the General Partner indicating that the Contributors dispute the
     circumstances giving 
<PAGE>
 
     rise to or the amount of 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 Contributors pursuant to such Article
     XIV. If, after receiving timely notice of a dispute hereunder from the
     Contributors, the General Partner fails to so submit the matter for
     arbitration within twenty (20) days after receipt of such notice from the
     Contributors, then the Contributors shall be relieved of the claimed
     indemnification obligation described in the Indemnification Notice. In the
     event the Contributors (i) receive an Indemnification Notice and fail to
     timely deliver notice to the General Partner of their dispute as to the
     indemnification obligation and fail to make payment within thirty (30) days
     after delivery of an Indemnification Notice or (ii) have 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 do 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 Contributors, to have acquired from the
     Contributors 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 Contributors), 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 Contributors under paragraph 10 hereof. In
     the event the Partnership shall have acquired from the Contributors any
     Collateral pursuant to this paragraph 11, the General Partner shall deliver
     written notice to the Contributors within ten (10) days thereafter
     identifying the specific Collateral acquired and, if such Collateral
     consists of Partnership Units, the Percentage Interests of the Contributors
     following such acquisition. Unless and until the Partnership shall have
     acquired from the Contributors 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. Each
     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 
<PAGE>
 
     the Contributors prior to such date, then on the first day immediately
     following the resolution of such Notice of Breach) the Contributors 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 Contributors, shall promptly execute and deliver any
     document or instrument reasonably requested by the Contributors 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 any Contributor shall not be
limited to such Contributor's Collateral.

     13.  Restriction on Transfer.  In connection with the security interests
          -----------------------                                            
granted by each Contributor under paragraph 11 hereof, each of the Contributors
agrees that any shares of Common Stock and any portion of such Contributor's
Partnership Interests included in the Collateral shall not be Transferred
without the consent of the General Partner; provided, however, that each of the
Contributors 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 a 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 a Contributor included in such 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
Contributors prior to such date, then on the first day immediately following the
resolution of such Notice of Breach) the Contributors 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 Contributors, shall
promptly execute and deliver any document or instrument reasonably requested by
the Contributors 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 each 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.
<PAGE>
 
     IN WITNESS WHEREOF, the parties have executed and delivered this Amendment
as of the date first above written.

                         WEEKS REALTY, L.P., a Georgia limited
                         partnership

                         By:  Weeks GP Holdings, Inc., a Georgia
                              corporation, its Sole General Partner


                              By:  /s/ Forrest W. Robinson, President
                                   __________________________________
                                   Forrest W. Robinson, President


                         CONTRIBUTORS:


                         /s/ THOMAS M. BECKMAN
                         _______________________________ (SEAL)
                         THOMAS M. BECKMAN

                         Address:
 
 


                         /s/ THOMAS B. FOWLER, JR.
                         _______________________________ (SEAL)
                         THOMAS B. FOWLER, JR.

                         Address:
 
 


Solely to evidence its agreement to its
undertakings in Exhibit D hereto:
                ---------        

WEEKS CORPORATION

   \s\ Forrest W. Robinson, Vice President
By:_______________________________________
   Forrest W. Robinson, Vice President