Dear heart, don't "give up" but build boundaries. STRICT boundaries - no more paying his way, especially if he's living elsewhere. If he's living under your roof, then you have every right to set strict boundaries and expectations, regardless of whether he's 20 or 120. It's YOUR home, and YOU make the rules. If he's NOT living under your roof, then you have no business paying ANYTHING for him, especially if he's living with a girlfriend, somewhere. If he's going to pretend to be an adult, then he can assume the responsibilities of BEING an adult - this is not a game, and he's not permitted to play-act that he's an adult without experiencing the consequences for his actions and decisions.
My eldest son is a diagnosed sociopath, and the only thing that I could do to avoid losing my sanity was to completely remove myself from his life. I cannot help him, I cannot cure him, and I cannot even "be there" to support him. So, unless your son is a diagnosed sociopath, there is HOPE that he'll learn from his stupidity - we were all young, and we've all made really stupid decisions. But, that doesn't mean that we, as parents, must allow the stupidity, especially when it is deliberately harmful to us or others.
The best thing that you can do for yourself is to have NO CONTACT for the present, especially with Miss Thing. No contact means no phone calls, emails, text messages, discussions, etc....and, this includes via third parties. Do not allow yourself to be drawn into the drama/trauma that is being created. This drama/trauma can not only become highly addictive, but it is thoroughly counter-productive and utterly negative. Walk away from the whole mess, let your son know that you're available when he's come to his senses, and involve yourself in something positive to keep your mind from wandering into the "woulda-shoulda-coulda" arena of parenthood.