$25 NLHE 6-max: Cold Called 3bet with AA, flop sizing help

PokerStars - $0.25 NL (6 max) - Holdem - 5 players
Hand converted by PokerTracker 4

UTG: 28 BB (VPIP: 25.00, PFR: 0.00, 3Bet Preflop: 0.00, hands: 4)
CO: 119.84 BB (VPIP: 42.86, PFR: 20.00, 3Bet Preflop: 0.00, Hands: 37)
BTN: 123.64 BB (VPIP: 34.38, PFR: 18.75, 3Bet Preflop: 10.00, Hands: 34)
Hero (SB): 97.64 BB
BB: 53.36 BB (VPIP: 33.33, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 37)

Hero posts SB 0.4 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.4 BB) Hero has A:diamond: A:club:

fold, CO raises to 3 BB, BTN raises to 10 BB, Hero calls 9.6 BB, fold, CO calls 7 BB

Flop: (31 BB, 3 players) 4:heart: Q:spade: 7:spade:
Hero checks, CO checks, BTN bets 12 BB, Hero ???

What do you raise to on this flop?

Reason for flatting and not cold 4 betting is that 4 betting probably gets a fold almost always pre so I prefer to 4 bet a hand like AK here. Both villains are also pretty fishy and I'll feel comfortable getting AA in on almost all flops but villains 1/3rd pot sized bet really threw me off and made me unsure of my flop move.

i'd raise all in, since any serious raise pot commits you for all turns anyway

I think any play is fine (besides folding), but raising is probably the most +ev play. All of his bluffs will likely shut down on the turn, and the seemingly safe board on the flop could change pretty quick.

Well if you are going to flat pre then you should normally be looking to CRAI on the flop, but his small bet on the flop does make that a bit big. You are still going to get paid by KK AQ if you shove.
We have 87bb behind, you could bet 30-40bb and get the rest in on most turns.

I would just overbet shove the flop and let flush draws, KK and AQ hands call you. If someone happens to have QQ then it sucks but that happens sometimes.

I think we're getting it in here anyway. I'd make my standard x3 raise, so 36BB, and then a shove on the turn for what will likely be about half-pot.