I'd go for a check/raise here, you're both deep and that's really the only way for a good shot at his stack. If he has a set or two pair I'm guessing he'll bet out and maybe he'll bluff with a missed flush/straight draw which I think is his most likely holding. The hands he'd check behind here with are probably missed draws which won't call another bet anyway or 1 pair hands. It's hard to put him on a queen.. the only hand he might call another bet on the river with but not bet himself are an overpair or maybe AJ but not sure if he'd even call with that unless he sees you as really aggressive.

edit: didn't really notice the huge overbet on turn, I guess if he'll call that overbet a push or close to it is fine