Marriage itself is defined as an interpersonal relationship that is intimate and usually sexual in nature, but is acknowledged as such. By definition, acknowledgement of such a relationship can be done by the state. It's a legal contract in government terms, and is usually formalized by a ceremony. Whether or not it is sanctioned by the church doesn't change the definition.
Morality isn't objective, however. That's the flaw in your argument. It wasn't implanted via birth or anything, it was ingrained via the social environment. There are a lot of individuals in the southern states (particularly Texas) that are for the 'death penalty' which is a form of murder. I'd say the closest you can come to objectively ethical is avoiding bringing harm to another human being, directly or indirectly. However, there are other definitions for this.
You may believe that morality is objective, but that doesn't change the fact that it truly isn't, since everything is relative to both perspective and situation. Let's say you're protecting people from a genocidal regime. They are searching houses. They inspect your house, and the people you are protecting are hiding under the floorboards. They ask you: are you hiding anyone? You answer: No. You just lied to them, but is it unethical or immoral to do so? Lying to someone dangerous in that kind of situation to protect someone isn't immoral.
Your definition of marriage, however, is strictly for procreation. This is a very subjective definition. The legal definition is different. Having marriage recognized by the state shouldn't bother you, though, since it has absolutely nothing to do with your own marriage.
"It does me no injury for my neighbor to say there are twenty gods, or no god. It neither picks my pocket nor breaks my leg." Thomas Jefferson, Notes on Virginia, pg. 159.
Essentially, what I'm referencing is that you should have no qualms with someone you don't know doing things that can't possibly hurt you.