well, if you fire the last barrel here, what sort of hands will he call/raise with?
obviously he's never folding two pair here, though i doubt he'll raise most two pairs on this board.
he's never folding hearts. He's never folding KT if he managed to backdoor himself into it
[Tc] ftl.
he probably won't fold an ace if he decided to float you on the flop with the overcard.
There's also a chance he'll station it up with
Xc, though that's not very likely.
He should be folding everything else. Jx is going to be *very* hard to call with here, and will be a long run losing call. those are great runners to get Jx - or really any other flopped pair that hasn't improved - to fold. Obviously he needs to be folding clubs here. And of course it's always possible he was floating you the whole way hoping to bluff if you ever showed weakness.
So this is tough. there's a lot of hands he could have, but we have very little real info on his hand. All he's done is float in position so far. Not exactly a whole lot you can get about his range from that.
Still, I think you're right. this is probably a good spot to fire a third barrel. He could have decided to peal one more card with a *lot* of hands on the turn, almost all of which beat 9 high, and a lot of which will fold to solid aggression. I think $76 is a good bet here. it's not so much that you're losing a grip when you're wrong, but it should be strong enough to get him to fold a lot of his range.
If he does call, make sure that you use it to your advantage. make sure that you make a note about how he might think you'll barrel light. And then make sure that the next time you fire on the river, you do it knowing that he's not going to believe you very much.