EXHIBIT (b)

Certification of CEO and CFO Pursuant to

18 U.S.C. Section 1350,

as Adopted Pursuant to

Section 906 of the Sarbanes-Oxley Act of 2002

In connection with the Report on Form N-CSR of Guggenheim Equal Weight Enhanced Equity Income Fund (the “Issuer”) for the period ended December 31, 2014 (the “Report”), Donald C. Cacciapaglia, as Chief Executive Officer of the Issuer, and John Sullivan, as Chief Financial Officer, Chief Accounting Officer and Treasurer of the Issuer, each hereby certifies, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that, to the best of his knowledge:

(1)   the Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2)   the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Issuer.

Dated:                 March 6, 2015                                          

                            /s/Donald C. Cacciapaglia                       

Name:                 Donald C. Cacciapaglia

Title:                   Chief Executive Officer

                            /s/John L. Sullivan                                   

Name:                 John L. Sullivan

Title:                   Chief Financial Officer, Chief Accounting Officer and Treasurer