Ignition No-Limit Hold'em, $0.05 BB (6 handed)
CO ($5.05)
BTN ($4.97)
Hero (SB) ($6.00)
BB ($4.43)
UTG ($3.11)
MP ($4.20)

Preflop: Hero is SB with A, K
UTG raises to $0.15, MP raises to $0.40, 2 fold, Hero raises to $0.92, 2 fold, MP calls $0.52

Flop: ($1.95) 8, 8, 2 (2 players)
Hero checks (?), MP checks

Turn: ($1.95) 9 (2 players)
Hero...?

Thoughts
PF: Standard 4-bet PF IMO, even against an UTG raise and MP 3-bet. I typically try to 4-bet between 2.2x - 2.5x of the 3-bet amount. Maybe I could have gone a little higher in retrospect since these two are more likely to be fish (they're both shortstacked and MP's 3-bet size is a little small).

Flop: I was trying to figure out at game speed whether I have a checking range on this flop or if I range bet everything. I think I check some things like AA-QQ occasionally so that I can check AK in this spot.

I feel like betting doesn't get him to fold anything better (at least not to one barrel, and I'm not sure if it makes sense to fire two with a hand that has some SDV). He probably shouldn't float me light in a 4-bet pot with too much worse either, and so turn spots are really awkward when I bet flop and get called.

Turn: Since he checks back flop, I start to heavily discount overpairs, as I think those generally bet for some mixture of value and protection. I don't completely remove them from his range, but it feels like his range is now largely weighted toward Ax hands. Do we try to induce from hands that usually only have 3 outs? Or do we bet and try to fold something that has 3 outs (plus maybe the other 9 chopping AK combos)?

I guess this is all still assuming the flop check makes sense in some capacity. I'm really curious about everyone's flop -> turn plans here.

I don't think we need to be range betting versus a random fish. AK destroys villain's check/folding range, so I don't see much point in betting. This villain is basically always betting stronger hands and checking weaker ones (or ones you chop with).

At the turn, I think villain's range is pretty much just overcards that you dominate. You never know with fish though. I think checking and betting small are both fine.

I would continue with maybe 1/4 pot bet on flop with my whole range on that flop. I think that villain still has 99-JJ here in check backs.

I would check/call the turn as you have a bluff catcher. Betting makes no sense as only better hands will call. If he checks back the turn I would check/call the river (still only a bluffcatcher). Depending on villain I might fold to a a river bet following a half pot turn bet by villain.