Notes preflop: Didn't feel like 3 betting AKo preflop because I felt BTN had a pretty tight range and I wanted the cutoff to come along with his/her remaining 27 BBs.

Merge - $0.10 NL - Holdem - 8 players
Hand converted by PokerTracker 4

BTN: 102.5 BB (VPIP: 18.39, PFR: 13.79, 3Bet Preflop: 0.00, Hands: 87)
Hero (SB): 130 BB
BB: 140 BB (VPIP: 13.33, PFR: 10.00, 3Bet Preflop: 4.76, Hands: 60)
UTG: 39 BB (VPIP: 0.00, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 2)
UTG+1: 14.3 BB (VPIP: 15.44, PFR: 6.88, 3Bet Preflop: 3.27, Hands: 837)
MP: 126.5 BB (VPIP: 19.28, PFR: 9.18, 3Bet Preflop: 2.34, Hands: 416)
MP+1: 152.8 BB (VPIP: 24.60, PFR: 7.14, 3Bet Preflop: 2.08, Hands: 128)
CO: 27.6 BB (VPIP: 31.06, PFR: 3.79, 3Bet Preflop: 0.00, Hands: 132)

Hero posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has A K

fold, fold, fold, fold, CO calls 1 BB, BTN raises to 4 BB, Hero calls 3.5 BB, fold, CO calls 3 BB

Flop: (13 BB, 3 players) 9 2 8
Hero checks, CO checks, BTN checks

Turn: (13 BB, 3 players) 4
Hero checks, CO checks, BTN bets 7.5 BB, Hero calls 7.5 BB, fold

River: (28 BB, 2 players) Q
Hero checks, BTN bets 14 BB, Hero ??

3bet preflop. Your excuses for not doing so are nonsense. (Button's range is not tight and why would you want to play a bloated multi-way pot OOP with a hand that's going to miss the flop 2/3 of the time and you won't have initiative or any idea where you stand?)

As played, fold turn. Check/raising has some merit if you had some reads or cbet stats. But I have no idea why you're turning into a calling station OOP against a "tight" range with Ace-high.

Don't you think BT would c-bet with all his overpairs on the flop?

Thus I assume OP thinks BT is betting here with whiffed overs, since op has the best whiffed overs certainly doesn't seem like he should be folding to a turn bet.

CMAR is right. The button wasn't tight.

IT666 is right as well. Results in spoiler for those interested.

3-bet pre and go from there. Probably the only hands that do best by calling in that spot are JJ-88, but I think I'd 3-bet TT+/AJs+/AK by default, and fold almost any other unpaired hands.
Post flop is a check-fold on the turn.

Flatting to keep the fish in the pot is a good reasoning. Depending on the level of ******edness of CO I could flat myself with AK/JJ+ and donk lots of flops.

But being oop in a mw pot sucks. If fish was HJ, the BTN on the CO and you on the BTN then flatting would be very reasonable. Here, you probably need better reads.

Would you bet this flop if checked to Babar? Assuming positions were same as in your example

Probably not with AK. Most of CO's range would be give ups but most of them would have very low equity and RIOs against AK anyway (he has lots of Ax/Kx that we could get value from if we hit the turn).
And this flop certainly hits the fish's range. Having the Ad is good but not good enough to bet vs fish.

Pre is bad. It's fine if btns a tight player but not when they're opening otb where their range is widest. Turn and river are fine / whatever