This is about affirming the worth of our relationships. No, it isn't; it's about equal protection of the laws. Our relationships have worth that doesn't need affirmation from big government. Also, government has neither the power nor the moral right to make people like us; rather, it can and should give us equal freedom.
Legalizing same-sex marriage will allow us to form more lasting, committed relationships. The magical piece of paper is neither necessary nor sufficient for a lasting, committed relationship. Some same-sex couples have been together for decades without it. Some straight marriages have gone down the toilet almost immediately. Again, the issue is equal protection of the laws.
Statistics show that marriage is good for people. The people quoting those statistics seem to have confused correlation with causation. It's more likely that people who tend to live more stable, productive lives also tend to want to marry.
This has nothing to do with legal recognition for polyamorous relationships. Why not? When people raise the bogeyman of legally recognized polyamory, I prefer to remind the advocates of "traditional," "Old Testament" marriage what tradition and the Old Testament actually say about polygamy. They either clam up or backpedal furiously. Once, when someone said that all moral people agree that polygamy is bad, I scored points by responding, "Then the Old Testament patriarchs must not have been moral people."