I am not positive, and too lazy to research it, but am guessing when the constitution was written, marriage was something that happened in a church and just a religious ceremony and because of that, they never intended government to have any say one way or another... I would argue the government stepped over constitutional boundaries when they started collecting marriage license fees.
Government-issued marriage licenses date until at least 16th-century England, and were a feature of every colony before the revolution (and every state at the time the Constitution was enacted)