Child support laws vary from state to state. You should talk to a
lawyer in Virginia to get reliable answers.
That being said, I doubt you will incur a child support obligation
simply by marrying the child's mother. Child support is an obligation
of the child's parents, which you are not (at the moment). If you were
to adopt the child as your own, then you would incur a support
obligation. I don't know what you have in mind by the "etc" you wrote,
so I can't comment on that.
You also might incur a spousal support (alimony) obligation by marrying.