Marriage is not just a social agreement, it is a legally binding contract. This is why, when a marriage is dissolved, property and custody become issues of law, because a contract is also being dissolved. Business contracts as well as marriage contracts in one state must be recognized in all states. If a marriage was only legal in the state of origin, people would have to get married in each successive state they lived in. Full Faith and Credit allows us to move and travel as we wish as married couples.
This has also created a legal issue, however, in that same sex marriage is legal in some states. So under the same clause of the Constitution, all states, whether they legalized such marriages or not, would be required to recognize the contracts as valid. Not to do so could be interpreted as a violation of the FF & C clause, but also of the 14th Amendment guaranteeing equal protection for all citizens under the law. This is what has led to the nationwide controversy and efforts by some legislators to pass the "Defense of Marriage Act" more clearly defining marriage as being between heterosexuals only. Ultimately, it will be the courts that decide.