Who deserves the legal right to choose my marriage partner for me?
A "Yes" answer puts us in our current state in which the purpose of marriage is left up to the individual. A "No" answer suggests that marriage exists for some external or greater purpose. People frequently suggest procreation. If marriage really is about procreation, then your marriage partner really shouldn't be up to you. The Eugenics Board (or Marriage Broker in the case of old-fashioned arranged marriages) will find the best suitable mate for you, and there you go. "No" may also include stipulations that people have sufficient mental capacity as to handle some of the ramifications of being married (see below).
•My Partner (i.e. the person I'm marrying)
A "Yes" answer here again puts us in our current state, this time focusing on there being no marriage without consent from both parties. A "No" answer, historically, implies that women are chattel, to be bought or sold as their parents/husband pleases. Not sure under what other circumstances you could answer "No" here but "Yes" above.
Lots of people keyed into the idea that children maybe shouldn't be able to get married without their parents' consent. Outside of that circumstance, we generally don't like the idea of living in a patriarchal society, so most people answered "No". Lots parents, of course, would try to change their children's answers to "Yes". I have a cousin whose parents threatened to disown him when he engaged the girl of his dreams.
This one opens up a bunch of cans of worms. Most people simply cannot separate the idea of marriage as a legal document and marriage as a religious practice. We'll eventually get traction on this issue because, put simply, anybody is free to join my religion just long enough for me to officiate their marriage if that's what they want. Hell, I'll officiate your marriage even if you don't want to join my religion.
•John Q. Public, Anytown, My State
Curiously, everyone seemed to think this was none of John's business, yet this is exactly what Equal Marriage opponents in Massachusetts are thinking. They're trying to put forward a public referendum on Marriage Equity. They want to ask Alan Klein of Osterville, MA if it's ok for me to marry a man. They want Irene Ballantine of Chelmsford, MA to tell me if I have that right. Yes, technically, that's one way to operate the State Government (see below on the State's role), but, semantically, I see no difference between a referendum on "whether members of the same gender can marry" and "whether Greg can marry his girlfriend".
•My State Government and My Federal Government
Yes, as a legal institution, Massachusetts does have to have some ability to regulate (legal) marriages, so it does need to "approve" them in some fashion. Yet most people seemed to think there is a limit. Does THE STATE have the right to approve/allow/encourage/enforce marriages based on criterion of race? religion? mental capacity? physical health? socioeconomic status? gender? sexual orientation? reproductive capacity? age?
In the eyes of the law, Marriage is first, foremost, and only a legal contract. Some say it exists to encourage and enable procreation, but when you pin them on it, they (usually) concede that procreation shouldn't be a requirement. This question really goes back to What is the Government for? If the Government's job is to guide how we live so we can be happy productive citizens, then yes, start hiring the Eugenicists. They'll make sure that, in a few generations, we'll be as happy and productive as Scientifically possible. But, in my eyes and I believe in those of the Founding Fathers, our Government exists to handle those tasks that require too much work for a single person to handle, whether they require too much expertise (FDA), coordination (national defense), or expense (highways).
The U.S. Government exists to serve us and make our lives better, as we as individuals define better. Legal Marriage is a service they offer to facilitate the commingling of assets and/or childrearing responsibilities and/or legal counsel. Only in circumstances in which the monetary risk of the Government offering a marriage certificate outweighs the costs of the individuals in question forming their own legal arrangement does it begin to make sense for the Government to not offer marriage.