JT, interesting turn card against PF raiser

[One Outer]

I find this hand interesting because there are I think there are lessons to be learned on multiple streets. I'm pretty sure I played this correctly (except for maybe preflop) but I want to submit it to the forum as a sort of check up because I believe that a couple of the decisions are close.

That being said onto the hand. Villain in this hand is sort of weak tight postflop. Earlier this night he called down AA on a T high rainbow board after catching a flop raise. Of course, his hand was good. Preflop is a different story; he will largely play correctly there (e.g., he's not one of these donks that limps QQ or whatever because he's scared of the flop).

Button is a TAGfish. He's one of those guys that plays only his starting hand value. For example he called a naked AK down earlier in the face of major aggression on two streets. His preflop ranges are TAG but he gets married to all his hands TT+, AK, AQ. He also kind of sucks postflop when he has an actual hand. I saw him check behind QQ on the river in one pot on a great board for his hand (J high, no flush, unlikely straight, paired deuces) against two fishy opponents that check called both the flop and turn.

Canterbury Park 6/12, full game

Hero is UTG+1 with J[img]/images/graemlins/spade.gif[/img] T[img]/images/graemlins/spade.gif[/img]

UTG folds, Hero limps, 1 fold, MP calls, HJ (Villain) raises, 1 fold, Button calls, blinds fold, Hero and MP call

Flop (4 players, 9.5 SB):

J[img]/images/graemlins/club.gif[/img] 3[img]/images/graemlins/spade.gif[/img] 9[img]/images/graemlins/heart.gif[/img]

Hero bets, MP folds, Villain raises, Button calls, Hero calls

I picked this line at the time because I wanted it heads up (why? I can't remember. This whole hand has me so lost.) and to see where I was at. I'm thinking that maybe I should have checkraised instead. I would love some discussion about this decision, particularly about c/r vs. lead and possibly putting Button on a hand.

Turn (3 players, 7.5 BB):

K[img]/images/graemlins/club.gif[/img]

Hero checks, Villain bets, Button calls, Hero...

I'm torn. I have picked up a gutshot but it makes my T outs dirty as hell and I hate that the Button is still in the hand. Villain clearly has something he is showing down, which means that he's way ahead. I also have to discount the T and Q[img]/images/graemlins/club.gif[/img] (but maybe not that much?). I have no idea what to do with my hand here.