HU: QT on AQQ Board

[BoxTree]

Commerce, 200 NL (Blinds: 3,5; 9-handed)

Hero has Q[img]/images/graemlins/club.gif[/img]T[img]/images/graemlins/heart.gif[/img] on the button.

Hero opens to $25. SB folds. BB calls.

Preflop Stacks:
Hero: ~$800
BB: ~$500

Flop (2 players, $50): Q[img]/images/graemlins/spade.gif[/img]Q[img]/images/graemlins/diamond.gif[/img]A[img]/images/graemlins/heart.gif[/img]

BB checks, Hero bets $40, BB calls.

Turn (2 players, $130): 7[img]/images/graemlins/club.gif[/img]

BB checks, Hero bets $80, BB min-check-raises to $160.

Okay, so what's going on here?

BB is a tight, mostly straightforward player. BB does all sorts of facial spasming before check-raising the turn. So I'm sure he has a monster.

What sort of monster? In order of current strength (but not necessarily likelihood):
AA
AQ
77
QK
QJs

I doubt he has 77. He may think I was making some sort of blind-steal preflop, but he's not going to call me all the way down with a pair of sevens on an AQQ board. So rule that out. He'd call the flop with QJs, KQo, AA, and AQ.

Of those hands, I'm only drawing live against KQ and QJ (okay, I have one out against AA). Against those two hands, I have three outs to the winner (the tens) and six outs to a chop (the aces and sevens).

He doesn't have AK, if you're wondering. He wouldn't min-check-raise the turn with TPTK on this board.

So, I figure I need to see the river to try to improve.

I call and the river is the miracle 2[img]/images/graemlins/club.gif[/img]. Ha ha.

He pushes.

Do I call the additional ~$275 (pot is ~$725 after he pushes)?