2/4 KK in blind battle, turn play question

[Tokyo!!]

Opponent is 20/15 and has been fairly aggro postflop. He hasn't been getting out of line. This hand wasn't played by me. Obviously I disagree with pf, and probably the flop, but I'm curious about turn play. What's a good range for the villain here? Call or dump it?

PokerStars No-Limit Hold'em, $4 BB (5 handed) internettexasholdem.com

Villain($436.60)
Hero ($390.40)
UTG ($629.50)
MP ($823.20)
Button ($678.60)

Preflop: Hero is BB with K[img]/images/graemlins/spade.gif[/img], K[img]/images/graemlins/diamond.gif[/img].
<font color="#666666">3 folds</font>, <font color="#CC3333">Villain raises to $16</font>, Hero calls $12.

Flop: ($32) T[img]/images/graemlins/club.gif[/img], 4[img]/images/graemlins/club.gif[/img], 6[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Villain bets $22</font>, <font color="#CC3333">Hero raises to $44</font>, Villain calls $22.

Turn: ($120) J[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
Villain checks, <font color="#CC3333">Hero bets $68</font>, <font color="#CC3333">Villain raises to $376.6</font>, Hero calls $262.40 (All-In).

River: ($827) 8[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players, 1 all-in)</font>

Final Pot: $827