KK laydown - preflop - UB 200NL

[Mur]

UB NL200, 10 handed. I've been at the table for maybe 40 hands. The villain in this hand had never gotten out of line and seemed pretty tight overall & passive.. He always got out of the way when big pots occured and never really left an impression. The hand, then my thoughts:

Hero $230 / Villain ~$150

Hero: Kd Ks
Pre-flop:

Player1 calls. Hero raises to $6. Player2 folds. Player3 folds. Player4 folds. Player5 folds.
Player6 calls. Villain re-raises to $21.
Player1 folds. Player6 folds. Hero re-raises to
$36. Player2 folds. Villain goes all-in for
$160. Hero folds. Villian is returned $124
(uncalled).

No rake is taken for this hand.
Villian wins $82.

Ok my thoughts. His initial raise could have been AA-JJ, possibly AK. In this game I really see AK calling and probably JJ as well. My reraise should narrow down my range of holdings for him, namely AA or KK. This doesn't appear to scare him one bit and he insta pushes.

Keeping in mind, this is UB 200NL - you don't see too many AK or QQ/JJ all ins.

Good fold or you play this different?