NL25 KK on dangerous board

[MickChecker]

Full Tilt Poker - No Limit Hold'em Cash Game - $0.10/$0.25 Blinds - 6 Players - (LegoPoker HH Converter)

Hero (SB): $24.75
BB: $53.10
UTG: $25.00
MP: $38.60
CO: $32.60
BTN: $25.60

Reads: <font color="blue">Villain was pretty solid, 19/11/8.0. Have not seen a dumb move from him so far.</font>

Preflop: Hero is dealt K[img]/images/graemlins/diamond.gif[/img] K[img]/images/graemlins/heart.gif[/img] (6 Players)
3 folds, <font color="red">BTN raises to $0.85</font>, <font color="red">Hero raises to $2.80</font>, BB calls $2.55, BTN folds

Flop: ($6.45) J[img]/images/graemlins/diamond.gif[/img] T[img]/images/graemlins/diamond.gif[/img] 3[img]/images/graemlins/heart.gif[/img] (2 Players)
<font color="red">Hero bets $5.00</font>, BB calls $5.00

Turn: ($16.45) 9[img]/images/graemlins/club.gif[/img] (2 Players)
Hero?

Ok, what to do here? Villain cold called my 3-bet, which limits his range to lets say TT+ and AK, I guess.
Do you fire again? Because thats pretty much commits us to the pot, right? So firing again would mean to shove which doesn't feel to good at this point, does it?