$5 NLHE MTT: AA vs flat in squeezed pot

Turn spot feels really awkward we cant really call turn with intention of folding river leaving ourselves 1/3 psb left? Do you just calldown in that spot without any reads hoping villain is overbluffing?
Hero (SB): 163,724 (46.8 bb)
BB: 67,454 (19.3 bb)
MP1: 152,182 (43.5 bb)
MP2: 201,038 (57.4 bb)
MP3: 455,976 (130.3 bb)
CO: 102,653 (29.3 bb)
BTN: 39,078 (11.2 bb)

Preflop: Hero is SB with A

A

MP1 raises to 7,000, MP2 folds, MP3 calls 7,000, 2 folds, Hero raises to 28,785, 2 folds, MP3 calls 21,785

Flop: (71,920) 7

Q

Q

(2 players)
Hero checks, MP3 bets 21,576, Hero calls 21,576

Turn: (115,072) 7

(2 players)
Hero checks, MP3 bets 34,522, Hero ???

uhm I think we just call down. it is a weird spot but given that we checked the flop villain can absolutely think a hand like 88-JJ is good.

Definitely calling the turn and check calling the river. Opponent could have a pair and is value betting but you don’t want to raise and have him fold those hands plus his bluffs. If he as a Q, then oh well. Don’t think you can fold.

Call down definitely seems fine to me. The 7 certainly shouldn't have hurt you very often. There's definitely some value hands they're betting that you beat.

cbet flop is better than check/call imho

I'd say we can cbet or check-call depending on the opponent.
But yeah, if you choose to call down vs an aggressive opponent, we can't fold on the turn.

U can't fold now, u're SPR<1 and with u're AA just move inn..

Inaccuracy postflop led to a misunderstanding after the turn. With a 1/3 pot bet, the villain gives you a good chance to call to get chips. Resetting a pair of AA would be much easier to re-raise after your raise on a double flop. Your check - call unleashed the villain of the hand and made it possible for an elementary bluff, even in the absence of his Q