It doesn't, which is the point I keep trying to make. Marriage isn't the real issue. It's a stalking horse. Homosexuality is the issue. Once you approve of one you have to approve of the other.
As for the Romans, they lasted 1,000 years because the pace of life back then was so much slower, without modern communications or transportation. It's probably equal to 200 years of today. It's widely understood that Rome collapsed because of moral decay. Just like us.
That's debatable. During the last century or so of the Empire, Rome experienced a period of nearly puritanical moralism.
In any event, the morals of the average Roman (as opposed to the morals of their leaders) didn't change much throughout the span of the Empire.
The entire agenda of gay marriage is about destroying the traditional family, NOT about gays getting "married."