The only way to put this to bed is to put it to a vote, let the public determine if the definition of marriage should be modified to include same sex relationships. Georgia has already had a voted related to gay marriage - back in 2004, in the GA Marriage Amendment.
Georgia Marriage Amendment, Question 1 (2004) - Ballotpedia
GA voted overwhelmingly change the state constitution to say that marriage is only between a man and a woman. 76% voted for it, and make no mistake, this sealed the chance of gay marriage being approved anytime soon.