From Justice Anthony Kennedy

"Many who deem same-sex marriage to be wrong reach that conclusion based on decent and honorable religious or philosophical premises, and neither they nor their beliefs are disparaged here. But when that sincere, personal opposition becomes enacted law and public policy, the necessary consequence is to put the imprimatur of the State itself on an exclusion that soon demeans or stigmatizes those whose own liberty is then denied. Under the Constitution, same-sex couples seek in marriage the same legal treatment as opposite-sex couples, and it would disparage their choices and diminish their personhood to deny them this right."

... and, in perfect summary:

"No union is more profound than marriage, for it embodies the highest ideals of love, fidelity, devotion, sacrifice, and family. In forming a marital union, two people become something greater than once they were. As some of the petitioners in these cases demonstrate, marriage embodies a love that may endure even past death. It would misunderstand these men and women to say they disrespect the idea of marriage. Their plea is that they do respect it, respect it so deeply that they seek to find its fulfillment for themselves. Their hope is not to be condemned to live in loneliness, excluded from one of civilization’s oldest institutions. They ask for equal dignity in the eyes of the law. The Constitution grants them that right." - Anthony Kennedy, for the majority.