15/30 river decision with AA

[Proofrock]

10/20 half-kill game at Northern Quest Casino in Spokane. It's a kill pot with the kill being posted by BB.

UTG+1 is loose preflop and will limp any suited connector, pair, suited ace, or two broadway cards preflop. He's pretty aggressive postflop when he hits TPTK+ and check/folds when he misses. He can be tricky and likes to check/raise the river when he hits his draws. Only hand of interest between us is when I checked behind with top two vs. his nut flush draw on a Q93T8 board.

SB is TAG who is steaming a bit after losing a few big pots.

UTG+2 is a bad, loose-passive player.

Preflop: UTG+1 limps, UTG+2 limps, MP limps, I raise on the Button with A[img]/images/graemlins/diamond.gif[/img] A[img]/images/graemlins/spade.gif[/img], SB 3-bets, UTG+1 calls, UTG+2 calls, MP folds, I cap, SB calls, UTG+1 calls, UTG+2 calls, BB folds.

Flop (17.6 SB): 8[img]/images/graemlins/spade.gif[/img] 2[img]/images/graemlins/diamond.gif[/img] 6[img]/images/graemlins/heart.gif[/img]
Checks to me, I bet, SB calls, UTG+1 calls, UTG+2 folds.

Turn (10.3 BB): 9[img]/images/graemlins/heart.gif[/img]
Checks to me, I bet and they both call.

River (13.3 BB): 5[img]/images/graemlins/diamond.gif[/img]
Checks to me and I ...?

Is this a check behind, b/f, or b/c, and why? This is probably a pretty straightforward spot, but even a quick one-line response would be appreciated. Thanks.