KK hand vs. 2p2er

[CalledDownLight]

Villain is BT2. I have him at 11.0/9.5/4.1 over 1800 hands. Basically he is a nit and doesn't get too far out of line. 4betting preflop is not an option. I think my flop line is standard too. What should I do on the turn here? Should I have led the turn? If you say shove please let me know what his range for calling is. If you call then what is your river line for a blank, K, J?

PokerStars No-Limit Hold'em, $2 BB (8 handed) Poker Stars Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

saw flop|<font color="#C00000">saw showdown</font>

<font color="#C00000">Hero ($400.75)</font>
UTG+1 ($176.15)
<font color="#C00000">MP1 ($211)</font>
MP2 ($142.75)
CO ($697.75)
Button ($209.30)
SB ($133.45)
BB ($199.75)

Preflop: Hero is UTG with K[img]/images/graemlins/spade.gif[/img], K[img]/images/graemlins/club.gif[/img].
<font color="#CC3333">Hero raises to $8</font>, <font color="#666666">1 fold</font>, <font color="#CC3333">MP1 raises to $26</font>, <font color="#666666">5 folds</font>, Hero calls $18.

Flop: ($55) J[img]/images/graemlins/club.gif[/img], 3[img]/images/graemlins/diamond.gif[/img], 6[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#CC3333">MP1 bets $35</font>, Hero calls $35.

Turn: ($125) 2[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#CC3333">MP1 bets $50</font>, Hero ???