Is marriage a private affair between a man and a woman? How are others involved?
In the United States, at least, we tend to think of marriage as a private affair, particularly since the notion of privacy has been read into the United States Constitution. However, historically and even today, there are many important community and societal interests in the marriage of two people, whether they be a man and a woman or two people of the same sex.
One important community and societal interest is in the offspring of any marriage. When people separate or divorce, it is important to the community and society generally that children are properly cared for, which is why the standard for determining what happens to children when a marriage is unraveling or is over is "the best interests of the child." At this juncture, certainly, marriage becomes a very unprivate affair, with adjudication by the court, which represents the state and the values of society.
Historically, and still, in some cultures, marriages were and are arranged by the bride and groom's families, often to consolidate wealth or to cement some business relationship. Thus, there are interests to be served that are well beyond any private relationships or preferences.
The ownership and disposition of property in a marriage is also of community and societal interest. The state claims an interest in marriage to the degree that it provides for the holding of marital property in a way that keeps it safe from individual creditors of either partner in the marriage and that allows property to be passed on to a surviving spouse without being part of an estate, with significant tax advantages. In many states, a surviving spouse may not be completely disinherited, permitted to claim some widow or widower's portion of an estate. Other benefits can accrue to a marital partner, for example, Social Security or veteran's benefits. All of these elements of marriage take it out of the private realm and into the "public" realm, since all of these represent policy decisions that are either subsidized by taxpayers and/or that represent some societal value. If marriage were strictly a private affair, none of these benefits would exist.
Our society has determined that marriage is a public affair by requiring one to get a marriage license and have a marriage ceremony performed only by various approved public servants, for example, judges, with witnesses present, for a civil ceremony. Even for a religious ceremony, the state requires that the marriage ceremony be done by legitimate clergy. These requirements take marriage out of the private realm as well.
Two other common state requirements, historically, were waiting periods and blood tests, to be sure the parties had no sexually transmitted diseases. Since each state has its own laws, I do not know which, if any, states still have such requirements. But these, too, are evidence of important societal interests, in not spreading disease and in having a "cooling down" period for those impatient to marry.
There are many elements of marriage that are private, but I am not aware of any society in which there is not some public interest in regulating marriage in some way. Marriages provide stable units in a society, consolidate wealth and interests, create progeny, and thus, society has an important stake in marriage.