What is really at issue here--IMO, at least--is adoption. If we allow homosexuals to call their "thing" marriage, we might assist in opening the door to adoption of children by homosexuals.
You might think of "marriage," as involved here, as a trademark. The state has decided to make the use of this "trademark" a requirement for adoptions that are organized by the state. Therefore, the state is a party to a marriage contract in a way.
I don't object to homosexuals doing whatever they please with each other, as long as they do it on their own property and no one can see or hear them. But they shouldn't call it a marriage, because that's not what it is.
This nation has the moral authority because this nation is a Republic, and the people have granted it that moral authority.
You might have rather asked why it should have such authority. It should have such authority because this state can not exist without a firm family foundation upon which to rest. Something called America (or Massachusetts) might continue, but it would not be what it has been up to now.
Those of us interested in preserving our nation (rather than just looking out for ourselves) will continue to argue for the state's interest being served by a common morality, which does not include letting sickos live together and calling it a marriage.
Shalom.