Big Draw vs Squeezer +1

[SGS]

I have seen villian squeeze a couple times, but not really do anything else outta line. Pre-flop might be debatable, but I figured I had position on him and it would probably go 3-way. What is your line here? Do you bet? And if called do you shove turn? Or are you just checking here hoping button will bet and u can go all in? Checking and trying to make ur hand? What you guys think?
Full Tilt Poker - No Limit Hold'em Cash Game - $10/$20 Blinds - 6 Players - (LegoPoker Hand History Converter)

SB: $2,416.00
BB: $2,000.00
UTG: $587.00
MP: $437.00
Hero (CO): $2,507.00
BTN: $2,252.00

Preflop: Hero is dealt J[img]/images/graemlins/heart.gif[/img] Q[img]/images/graemlins/heart.gif[/img] (6 Players)
2 folds, <font color="red">Hero raises to $70.00</font>, BTN calls $70.00, SB folds, <font color="red">BB raises to $260.00</font>, Hero calls $190.00, BTN calls $190.00

Flop: ($790) T[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/club.gif[/img] 5[img]/images/graemlins/heart.gif[/img] (3 Players)
BB checks, Hero???

SGS

[Unknown Soldier]

keep betting til you run out of chips

[DrMagic]

/\

[nextgenneo]

$580 to go and hope he doesn't have A[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/heart.gif[/img]

I'd prob fold preflop but you are in position and know he has a fairly wide range so its probably okay.