The basis for 'rights' is that anyone should be able to live their life free of fear of harm and oppression. Gay marriage is just the most recent branch of an ongoing attempt to have the majority of Americans just leave gay people alone and let them live their life in peace. You seem to be under the impression that gay people exist in a vacuum where marriage is the only thing they can't do. Restrictions on marriage are just the latest in a long list of barriers that have to fall in order for gay people to have the same rights the rest of us have.
My belief is that opposition to gay marriage is indicative of an objection to the idea of gay people themselves, since nobody who has any issues with gay people being gay has issues with gay marriage. It's just a thin veneer of respectability bigots put on in order to appear more civil.