I would do the betting on the turn here since the lightest the villain is floating you here with is XcYc, imo, and he could check back and take a free card. Doing the betting also allows you to fold and avoid this tough river spot as he will be compelled to RRAI with his better hands more often and will check back his Qx on the river for showdown value.
I think the river is entirely dependent on bet sizing; as played, I see no point in betting. If you bet small and he shoves, what are you going to do. If you shove, he'll snap you off with a large amount of crap he beats you with, but probably not KT. OTOH, he may bet for thin value with KT as your line looks so much like a QT.
Barry