TT played wrong

Villian is a thinking player and seems mildly aggressive.

Ultimate Bet 1/2 Hold'em (10 handed) FTR converter on zerodivide.cx

Preflop: Hero is MP2 with T[img]/images/graemlins/spade.gif[/img], T[img]/images/graemlins/heart.gif[/img].
<font color="#666666">4 folds</font>, <font color="#CC3333">Hero raises</font>, <font color="#666666">2 folds</font>, Button calls, <font color="#666666">1 fold</font>, BB calls.

Flop: (6.50 SB) 7[img]/images/graemlins/heart.gif[/img], 8[img]/images/graemlins/heart.gif[/img], 2[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(3 players)</font>
BB checks, <font color="#CC3333">Hero bets</font>, <font color="#CC3333">Button raises</font>, BB folds, <font color="#CC3333">Hero 3-bets</font>, <font color="#CC3333">Button caps</font>, Hero calls.

Turn: (7.25 BB) J[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#CC3333">Button bets</font>, Hero calls.

River: (9.25 BB) 7[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#CC3333">Button bets</font>, Hero folds.

Final Pot: 10.25 BB

My thinking is that he floped a set so I call the turn with the flush draw. Not making the draw I fold the river, which I think now was a mistake.

Also, should I have led the turn? Again since (in my mind) I'm playing for the heart, check/call seems right.