I may be wrong and dumb, but my thoughts ...

Preflop 3 bet is a no brainer.

On flop, check is standard. Raise by villain has a high percentage of being a bluff a lot of the time, or a Jxxx. So the x-raise represents a Qxxx. Not much of another way to win the pot, and this would be read-defendant and I'd think a x-fold would be right a lot of the time against certain players. 

The call is unexpected and interesting. A QJxx would not likely bet the flop. A Qxxx with good kickers may raise instead of call, although he may still call, fearing hero has QJxx. 

I think the only hands that lead the flop and call the raise here are Qxxx, Jxxx, and sometimes JJxx, although I'd think we'd see a re-raise from that on the flop a good portion of the time. 

So I think villain usually has Qxxx or maybe a thin bluff-catching defense with Jxxx. When the K comes on the turn, villain now is worried about QJxx, Qxxx with better kickers, QKxx, JJxx, ATxx, and KKxx. 

So, with all that I think we have to continue, because it's too disgusting to give up on the turn here with all that we can rep while at the same time opponent is unlikely to have QJxx, JJxx, KKxx, ATxx. He might have QKxx, but that's a chance you might have to take.

Now, the bet sizing I'm not sure about. Seems like if the read of Qxxx or Jxxx is right, then there is so much we can rep that he hates that he really can't call even that much. He's either going to have to push, which he hates to do given our range that has hit big hands, or fold. So we can make a cheap, smart play, and then finally give up on a call/raise. 

If my understanding of the hand is right (big if?), then it seems like a beautifully well-played hand.