Hoo boy...
I'd like to attempt to say a few things to hopefully get people thinking, and not really argue too much. (I don't think this conversation is terribly constructive at this point as far as I can tell.) I think my stance on it should be pretty clear. (Practicing Catholic :)
Let's get a little into social theory, etc. because that may actually prove to be somewhat constructive.
First of all, we should note that the family is the fundamental unit of society. In fact, family is a far more essential social structure than government. We can all think of situations where the government is, at best, largely absent (eg the "Old West"). The family is the primary place where children are raised and taught to live in society at large. It is the first place where they encounter others and learn how to get along with others. If that job is done well, the children are much more likely to become contributing members of society. Statistically, that tends to happen most often in an intact family of a mother, father and children.
Because the future of society depends on not just bodies existing, but upon educated, law-abiding citizens, it is in the society at large's best interest to incentivize and promote intact and loving families. Obviously, without people society doesn't exist. Without educated, law-abiding people, you have barbarism. You'd have either anarchy or dictatorships. Without virtue, then, you cannot have a well-ordered society that people like to live in that thrives.
Furthermore, family relationship is extremely important to inheritance and estate laws. Without state-recognized family relationships, the default option for inheritance becomes the state, as the state would recognize no relationships of its citizens other than their relationship to itself.
Insurance also is very tied to family relationships. Health insurance, life insurance, etc. all are restricted and guided by these family relationships.
So, there are a host of reasons that the state needs to recognize familial relationships and promote good, intact families. Fundamentally, promoting marriage is promoting the common good.