There is nothing in the U.S. Constitution about marriage. There are no federal regulations about marriage. No one in 1789 considered marriage an issue that should concern the government. Over the years individual states did pass laws pertaining to divorce and the federal government does recognize marriage in determining income tax payments and Social Security benefits.
Strict constitutional scholars will have a difficult time justifying regulations that define marriage. They could of course determine that just as legal marriage is authorized by local laws the definition of marriage can be defined by local law.
Proponents of gay marriage could argue that equal protection under the law also means the right of Americans to marry anyone they desire. After all marriage choice is personal and is in accord with the Declaration of Independence that reads in part: We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.
I personally do not find any attraction to my own sex except as friends. However, it will not impact my life one iota if people of the same sex prefer to marry.