Will SCOTUS Determine Bans On Same-Sex Marriage Unconstitutional?

In the upcoming session the Court will hear, Obergefell v. Hodges, a potential landmark case regarding same-sex marriage.  The Court is answering two questions: 1) whether the Constitution requires a state to license a marriage between two people of the same sex and (2) does the Constitution require a state to recognize a marriage between two people of the same sex when their marriage was lawfully licensed and performed out-of-state?

In recent cases the Court has addressed the DOMA (defense of marriage act) and found it unconstitutional because it barred the Federal government from recognizing same-sex marriages that were legalized under relevant State law.

It is long standing precedent that the right to opposite sex marriage is a fundamental right under the Constitution, the question is whether the Court will extend this same protection to same-sex couples.  Most commentators believe that the case will turn on the question as to whether the States have an legitimate interest in prohibiting same-sex marriage, and if so are these laws narrowly tailored to protect that interest.

Even if the Court finds that States have a legitimate interest in prohibiting same-sex marriages, and that laws banning are narrowly tailored to protect this interest, how are these states to handle same-sex marriages couples from States that have recognized same-sex marriages.  The Constitution contains a clause known as the full faith and credit clause which requires one state to recognize public acts of other States.  Thus, if a same-sex couple in Arizona moves to a State that does not recognize same-sex marriages, does that State have to honor the marriage as Arizona would?