As I was reading this thread I put myself in villains shoes. I would CB with AK 100% of the time on that flop, and he would too. As soon as he checks you have to be worried about a monster IMO (although a terrible play by him IMO, even though it worked)
I would have checked behind on the flop. I would bet the turn if checked to again. I would also call a reasonable river bet. As played I don't raise the river because I'm not getting called by a hand I beat. Villain either has a set, a straight, or a busted draw here 90% of the time. He never has AK.
Also, repopping preflop is very aggressive with KQ. If that is standard for this spot then I am out to lunch because I haven't seen that much, and would never do that unless villain was very loose. IMO a reraise with KQ is a bluff. Why not reraise 72o instead? That way you don't waste a bluff on a very playable hand in position.