No where in the Constitution does it set out any grounds for rules regarding marriage. So, by the Tenth Amendment, those rights are either reserved to the states or to the people. As of now, the states control the marriage of institution by requiring a license to be married. Only a priest (or justice, but that's another story) can marry someone, and the state can literally decide for themselves whether or not two people can marry. Should the government have this kind of power?
Of course not, that is absolutely insane; the government should never have this kind of power.
Marriage, as an institution, should be in the hands of the citizens. Essentially, we should "privatize" marriage. Relationships between two people are private, and not the business of the government. You shouldn't need a license to be married, and you shouldn't have to perform a religious ceremony to be married.
If we privatize marriage, then natural rights could emerge; especially for those who don't have them under the state-run marriage system. If a gay or lesbian couple wanted to get married, then they could because the government doesn't have the authority to say no. Same thing for every other type of relationship. No matter how bizarre they are, you don't have a right to legislate what you believe is the right form of marriage. These people have natural rights, one of which is the right to a personal relationship.
Marriage belongs in the home. There, two (or, I guess more) people can love and care for each other without having to go through a bureaucracy. People would be free to love as they please. Get the government out of marriage, and we will all be better off.