As played, I would probably fold the turn as Bobbo suggested possibly doing.

What I might do, however, if you were going to call bets on the turn and river like you did. . .is actually re-raise that flop. Maybe this is horrible, but I think he is capable of the line he played up through that c/r with something like QK or QJ as well as a set, doubtful he called a raise with a two pair hand to me. A re-raise would help find out where you are at - it will probably make KQ or QJ fold but was he really going to put an awful lot more in the pot with those hands anyways? Again this has its disadvantags though, maybe downright bad I dunno, I suck heads up too.