Who has the authority to define marriage? Does not that authority belong to God, who created marriage and defined it as the union between a man and a woman? He had the authority, and still has it unless he has delegated it to some portion of his creation. I am not aware that he has made that decision.
To the people he designed, created and continues to sustain, God has given much authority. For example, people can choose to attach benefits to marriage. People also have authority to create other formal relationships and contracts and to define them as they wish.
And the people can attach benefits to these new relationships and can remove benefits they previously attached.
People can attach the same benefits to civil unions as they attach to marriage. Or they can choose to attach different benefits.
People have the authority to design and create formal relationships, not including marriage, and to attach benefits to, and remove benefits from, all relationships. But if there is evidence somewhere that God has delegated to people his authority to define marriage, I'd sure like to see it.