KK Hand, difficult turn decision

[Inevitable]

Why did I check? Villian was 19%/3/.8 after 37 hands. I figured he had JJ, and I wanted to see what was up. It gets scary on the turn because it puts 4 to a straight, and he could have TT. I know it can't be QQ because he probably would have re-raised preflop. I'm looking to get some harsh criticism for both my flop and turn play. I was wondering if I should have re-raised for more preflop, and how I could've played the flop and turn better. Also, what would be done on the river had I stayed in?

PokerStars No-Limit Hold'em, $0.10 BB (9 handed) converter

MP1 ($5.45)
MP2 ($1.80)
MP3 ($7.90)
CO ($2.90)
Button ($0.70)
SB ($6.65)
Hero ($17.95)
UTG ($8.85)
UTG+1 ($14.85)

Preflop: Hero is BB with K[img]/images/graemlins/spade.gif[/img], K[img]/images/graemlins/heart.gif[/img].
<font color="#CC3333">UTG raises to $0.7</font>, <font color="#666666">2 folds</font>, MP2 calls $0.70, <font color="#666666">4 folds</font>, <font color="#CC3333">Hero raises to $1.4</font>, UTG calls $0.70, <font color="#CC3333">MP2 raises to $1.8</font>, Hero calls $0.40, UTG calls $0.40.

Flop: ($5.45) 8[img]/images/graemlins/heart.gif[/img], J[img]/images/graemlins/spade.gif[/img], Q[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(3 players)</font>
Hero checks, UTG checks.

Turn: ($5.45) 9[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(3 players)</font>
<font color="#CC3333">Hero bets $3</font>, <font color="#CC3333">UTG raises to $6</font>, Hero folds.

River: ($14.45) 6[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>

Final Pot: $14.45