The concept of " sin " is only a religious concept and an Abrahamic religious concept at that.
The heart/head dichotomy does not exist, so if your " mind " understands why gay marriage is wrong while your " heart " does not I suggest you engage your brain and logically asses the situation from a rational perspective.
You may find that your 3000 year old desert dogma has nothing to say about this issue worth considering and that gay predates religion by quite a distance. So, the truth, that gay marriage will happen, does not need your belief to be true and that something can be true, that the rights of gays supersede anything you believe, whether you believe it or not.