4/180 vulnerable hand becomes near-nuts

[Kimbell175113]

PokerStars No-Limit Hold'em Tourney, Big Blind is t30 (8 handed) internettexasholdem.com

MP2 (t2170)
CO (t1575)
Button (t7410)
SB (t1175)
BB (t3280)
UTG (t1460)
Hero (t3035)
MP1 (t1780)

Preflop: Hero is UTG+1 with J[img]/images/graemlins/heart.gif[/img], J[img]/images/graemlins/club.gif[/img].
<font color="#666666">1 fold</font>, <font color="#CC3333">Hero raises to t80</font>, MP1 calls t80, <font color="#666666">1 fold</font>, CO calls t80, Button calls t80, <font color="#666666">2 folds</font>.

Flop: (t365) J[img]/images/graemlins/spade.gif[/img], 9[img]/images/graemlins/spade.gif[/img], T[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(4 players)</font>
<font color="#CC3333">Hero bets t230</font>, MP1 folds, CO folds, Button calls t230.

Turn: (t825) 9[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero ???</font>

Betting builds a pot, and there's always a chance he'll shove over with a big draw.

Checking lets me get in a checkraise (which is necessary to get all the chips in, two streets of PSBs won't do it), and it lets him improve if he has a weak draw.

Any advice on what his range may be, and how best to extract ? If bet, how much?