Well, you're hand is pretty face up and he has zero FE on the river so he's not looking for you to fold. Probably fold the turn as played.

If he's a serial 3-better a small 4-bet might be a nice play to induce a push.

I really have no idea how to play these guys as I haven't encountered people like them yet in my weak-ass games. I'm pretty much just here to give HalvSame props on his awesome oneliner.