NL100 - KK on paired board against tight BB

[++Jojo++]

Prima Network No-Limit Hold'em, $1.00 BB (6 handed) Hand History converter Courtesy of PokerZion.com

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

SB ($48.69)
<font color="#C00000">BB ($392.80)</font>
UTG ($103.53)
MP ($91.42)
Hero ($98.00)
Button ($124.50)

Preflop: Hero is CO with K[img]/images/graemlins/heart.gif[/img], K[img]/images/graemlins/spade.gif[/img].
<font color="#666666">2 folds</font>, <font color="#CC3333">Hero raises to $4</font>, <font color="#666666">2 folds</font>, BB calls $3.

Flop: ($8.50) 9[img]/images/graemlins/heart.gif[/img], 6[img]/images/graemlins/spade.gif[/img], 9[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
BB checks, <font color="#CC3333">Hero bets $6.5</font>, BB INSTAcalls $6.50.

Turn: ($21.50) J[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
BB checks, <font color="#CC3333">Hero bets $12.5</font>, <font color="#CC3333">BB INSTAraises to $30</font>, Hero calls $17.50 with an uneasy feeling.

River: ($81.50) Q[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">BB bets $81.5</font>, Hero ask what to do here

<font color="blue">Villain: 20/7/1,7 (aggression increase over the streets) but stats doesnt seem so significant cause villain was running very nice over about 150 hands that I have.</font>
I ask me what kind of hand I beat on river and think that I am a dead duck. Should I shove it on turn? For myself I think this play smells like he had 66 or JJ.
How do you play this hand?

Thx
JO