DOMA as "a bare congressional desire to harm a politically unpopular group."

In United States v. Windsor, the Supreme Court finds that DOMA "violates basic due process and equal protection principles applicable to the Federal Government." (The constitutional text is the 5th Amendment which only says "due process," but the Court has long viewed "equal protection," which is explicit in the 14th Amendment, as implicit in the 5th Amendment.) Justice Kennedy writes for the majority:

The Constitution’s guarantee of equality “must at the very least mean that a bare congressional desire to harm a politically unpopular group cannot” justify disparate treatment of that group. Department of Agriculture v. Moreno, 413 U. S. 528–535 (1973).

The unpopular group to be harmed in Moreno was hippies. To understand the scourge of hippies as it was seen at the time, I highly recommend this 1971 NYT  article: "Ripping Off, The New Life Style" (citing the Jefferson Airplane lyric "All your private property is target for your enemy/And your enemy is/We-e-e"). Congress was hoping to keep food stamps away from hippies, and that didn't cut it.

So is keeping marriage away from gay people no better than denying food stamps to hippies?

In determining whether a law is motived by an improper animus or purpose, “ ‘[d]iscriminations of an unusual character’ ” especially require careful consideration. Supra, at 19 (quoting Romer... at 633). 

How is excluding gay people from marriage unusual? It's an old tradition. What's unusual is Congress horning in on an area of traditional state regulation:

DOMA’s unusual deviation from the usual tradition of recognizing and accepting state definitions of marriage here operates to deprive same-sex couples of the benefits and responsibilities that come with the federal recognition of their marriages. 

And there's "strong evidence" that DOMA had "the purpose and effect of disapproval" of same-sex couples.

The avowed purpose and practical effect of the law here in question are to impose a disadvantage, a separate status, and so a stigma upon all who enter into same-sex marriages made lawful by the unquestioned authority of the States.

That language about "stigma" and "a separate status" should be useful in challenging state law that creates "civil unions" for gay people, though the problem in Windsor was only about the federal government's refusal to recognize marriages that the states had validated.

... DOMA undermines both the public and private significance of state-sanctioned same-sex marriages; for it tells those couples, and all the world, that their otherwise valid marriages are unworthy of federal recognition. This places same-sex couples in an unstable position of being in a second-tier marriage. The differentiation demeans the couple, whose moral and sexual choices the Constitution protects... and whose relationship the State has sought to dignify. And it humiliates tens of thousands of children now being raised by same-sex couples. The law in question makes it even more difficult for the children to understand the integrity and closeness of their own family and its concord with other families in their community and in their daily lives.

Under DOMA, same-sex married couples have their lives burdened, by reason of government decree, in visible and public ways. By its great reach, DOMA touches many aspects of married and family life, from the mundane to the profound. It prevents same-sex married couples from obtaining government healthcare benefits they would otherwise receive....

Ultimately, the Court finds "no legitimate purpose" —  only "the purpose and effect to disparage and to injure those whom the State, by its marriage laws, sought to protect in personhood and dignity." Again, it's hard to see why the states' willingness to dignify these relationships is essential, but that's the question before the Court today. I don't think, in the end, that this is really very much about federalism, except as a steppingstone. This is a case about rights. Even though there's no heightening of the level of scrutiny, the Court aggressively characterizes the government's purported legitimate interests from the rights claimants' point of view and sees nothing but disparagement, denigration, and stigma.

ADDED: I'm just getting to the Scalia dissent saying the Kennedy opinion may "initially fool[] many readers... into thinking that this is a federalism opinion" and seeing no "point" in the long discussion of state power to define marriage other than — he guesses — to make a "pretense" that this case is only about limiting the federal government and "leaving the second, state-law shoe to be dropped later, maybe next Term." I said "steppingstone." Hopping across a stream, taking off shoes... the point is the same. It's a case about rights.