AA facing heat on monotone flop

10/25 HK$ FR game(small stake,10/25 sb/bb,500-3k buyin). Hero raises 100 from UTG with A A, BT calls,sb calls,bb calls.
BT: 9k stack, a postflop timid cautious bad regular who calls a lot preflop but knows when to fold TP hands.
SB:2.5k semi-loose passive
hero: 3.5k a TAG clean player
flop($400): Q 9 7 hero bets $200, BT raises to $500, SB calls $500, hero??

I can't imagine doing anything but shoving, but maybe that's bad.

I'd shove, but I got a bad feeling about what you ran into...

BT is a regular who would never call with any worse TP hands if i shove 140BB on the flop with less than 30% equity when he holds two clubs. Given his tendency, i took a passive line,flatted his minraise and kept their weak hands(maybe this is bad).Live players are silly enough to not bet correctly on the turn&river, So i want to exploit it.
flop($400): hero bets $200,BT raises to $500, sb calls, hero calls
turn($1900): 3 sb checks, hero checks,BT bets $700, sb calls, hero calls of course
river($4000): 3 sb checks, hero ?

you caught the best non club card in the deck, evaul his bet size obv.

Calling flop seems fine, check river.

I like how you played it based on reads.

River paired the board. Check could *very* easily be a scared flush along with all the hands you had crushed.

Check seems fine.

BT still to act and still has the most monsters in his range.

BT checked down with KcJc and sb showed Q9s.The regular said he feared somebody just hit river boat.