Marriage has never meant anything else. How can you constitutionally support changing what an institution is?
Like the meaning of any word, the meaning of the word "marriage" is socially constructed. Marriage practices have differed in many times and places. Sometimes it is arranged, sometimes forced, sometimes voluntary. Sometimes it is a political alliance, sometimes a commercial transaction, sometimes a civil contract, and sometimes a religious covenant. Sometimes it is done for love; sometimes with more mundane motivations. Sometimes it involves sexual union; sometimes it is strictly platonic. The point is, the idea that marriage is some sort of static institution that has always meant to everyone everywhere what it means to you is very naïve. In fact, the first same-sex marriages on record occurred around 300 AD among the ancient Romans. (Such marriages were probably considered extra-legal, but were certainly taken seriously by the participants.) But even if same-sex marriage were without historical precedent, it wouldn't matter. All social institutions possess a certain malleability, and can be (and frequently are) adapted to new cultural circumstances. To suggest that social changes are invalid if they are without historical precedent would exclude all of modernity and all religious sects of recent origin (including your own, despite its typically restorationist pretensions). To the contrary, historical precedent is irrelevant. At issue here is not the question of what marriage has meant to most people throughout history, but rather what it means to people today and whether they should have the right to define and practice it as they will. I believe they should.
Incidentally, I suggest that same-sex marriage redefines marriage only in subtle ways. Excluding a small number of bitter iconoclasts who hope to deconstruct marriage by treating it irreverently, the form and meaning of same-sex marriages are mostly the same as in other, more traditional American marriages. The difference lay in the gender of the participants and the possibility of issue. That's all. To say that gay-rights advocates are "changing what an institution is" assumes that the essence of marriage lay with the gender of the participants rather than with the symbolic, social, and sacred significance of the act. I think that if you really think about it, you will have to admit the gender of the participants has no necessary connection to the significance of the institution itself. I believe that people have a constitutional right to define marriage as they will, but I also suggest that the changes to the institution of marriage we will see at the social level will be much less dramatic and frightening than fundamentalist reactionaries would have us fear. Perhaps that should comfort as as we do the right thing, and legalize gay marriage once and for all.