And marriage would seem to fall within that boundary, at least for me. Two people are married, the State is not a party to that union. And since it's not a party, I wonder why the State should be concerned.

But the State (state as in government be it at the national state or local level) is a party of the marriage. Who issues the marriage certificates? Who certifies the ministers/officials that perform the unions? Who establishes the unions as having special rights and protections under the laws? In the case of divorce, who specifies that a couple is no longer a union and that those special right and protections are void?

The state.

If the state can have such broad powers as to determine who is considered legally married, then it seems reasonable to me that they also have some (not all) authority in limiting which couples may be married. Some reasonable limits on marriage would and do include kids, close genetic relations, and persons already married. Should we take the sate out of the equation, there would be no proper way to limit marriage as cited previously.