I am not great at reads in general, and even worse when I'm not in the hand itself, but here goes nothing.
Since you've reraised convincingly preflop, he might have put you on KK or AA and he probably doesn't have these himself because he would have been likely to reraise unless he avoids defining his hands like this too much.
He might be scared of trip kings and wants to find out by leading out at you with that half pot bet (bold move and he will def. get information by how you react).
By just calling you may have made him think that that is not what you hold. And since he min-raised from UTG preflop, reminds me of a small-medium pair trying to force out two big and big-weak hands.
When the Q comes I think he's already decided you have AA or AK, not KK or QQ. There
Of course you'll tell me he had AT,
but I think he has has a set but is worried about an overset. First guess JJ, second guess 44. But I lean heavily on the side of JJ.
I hate doing these because I hate being wrong
Never mind.
I'd have raised on the flop and if he'd have called or raised me I'd have thought about folding on the turn. Where you are now, I'd fold. But I'm quite conservative.