It is very interesting that you ask this question in this manner. I am not necessarily supporting anything I am typing, but looking at it from a historical and textualist perspective. The States' rights are implied in the Article IV of the Constitution, and the people's rights are stated in multiple places of the Constitution. But the 9th and 10th Amendment codify those rights, as for the States in a very broad fashion. Justice Alito's draft, suggested that the ruling on abortion would not effect other "constitutional rights" such as same sex, is questionable; i.e. he specifically saying it is not therefore it cannot be. But from a historical and textual perspective of the same-sex marriage ruling, the Supreme Court, by all means over stepped their authority. If you have ever attended a wedding, the person who officiates the wedding says "By the power vested in me, by God and the State of (insert State), I now pronounce you (insert appropriate description)" The power to issue marriage licenses is clearly a State power (especially since it is not listed as one of the powers of the Federal government in Article I of the Constitution). According to Article IV, Section I of the Constitution, it says all official documents by the States must are to be recognized with full faith, meaning my driving license will be accepted in any State that I travel in, same goes for a marriage license. So same-sex marriages, if they had a legal license, must have been recognized in all 50 States of the Constitution.
So, Alito's opinion, is very much a textualist opinion, who believes that the People and the State should have the ultimate say of what happens in their State. My state for example, passed a ballot measure on the whether abortions should be performed or not; and Roe v. Wade ignored and overthrow a ballot measure that received over 70% of the people support. So who's rights are being suppressed and who has the "greater right:"?
