This is a pretty horrible flop for us in a 4bet pot. A huge amount of a typical villains 4bet calling range is going to consist of QQ/JJ so I'm not sure if I like the flop c-bet at all. However, this villain has quite a low fold to 4bet stat, what kind of sample size is this based off of? Given that a lot of the likeliest holdings for villain would be JJ+ and AK, and keeping in mind that AK will more than likely be folding to our bet here we are only going to be getting value from a hand like KK. AQs is somewhat possible but not overly likely here I feel.

On the turn this is one of the worst cards for us, I think betting again here is a pretty large mistake. The unlikely AK has gotten there so it's only KK that we still beat. As tight as it seems I feel this is just a reluctant check fold on the turn. As played it's a pretty comfortable fold.

As played definitely fold to the turn shove. Pre and flop look fine.

On this turn when deciding whether to bet or not there's a couple things you should look at.
1) Where does AA fall in your range. In this spot you might have AK, KK, QQ, JJ, maybe TT and possibly a couple 2-pairs and maybe some flush draws. In terms of value hands AA falls near the bottom so it shouldn't be an auto-bet if you follow the guidelines of bet polarized and check medium strength hands.
2) What does villain's range look like? He can have a bunch of sets and this deep he can definitely have AK. There are also 2-pair combos and if he has a draw it's likely a pair+draw or combo draw so they'll have strong equity. Overall, definitely not a weak range so betting for thin value seems less attractive.

I would be checking turn and most likely calling turn folding river though that seems a bit thin too.

Tough spot as these always are, I think AA isn't looking amazing here.
I think you can check the turn and call a bet that isn't too large and if he goes nuts on river then fold. If he bombs the turn I probably even fold there and then though.
There's 2 pairs, sets galore out there and of course AK.

@Komododragonjesus Not much I could add to this one but I'd be interested to learn how we would play it IP. Would a chk behind be good on the flop or is a bet nearly mandatory? I just dislike boards of that texture in this situation and tend towards playing like I have a 2nd pair type holding.

Go bigger pre and get in a good sized portion of your stack. You are out of position and the more you can get in pre the easier the hand will be to play, as you lower the potential number of streets they can play and use their positional advantage effectively. I would go to at least $8.50 - $9. Many people will and have disagreed with this thought, but I do strongly advocate bigger 3b / 4b than seem to generally take place. It makes it so much easier for stacks to go in and we can reduce it to a two street game. As you have sized it pre flop and turn you put yourself in a awkward spot where you have ~ $30 back into ~$75. Going bigger pre allows you to bet flop and shove turns board dependent. Given their 3b call range really crushes this flop, we could elect to check it and reduce it to a bet turn bet river type line for two streets if we decide to go for value. The small flop bet is asking for trouble I think also. Sub 1/2 pot in my mind in these spots when I see it I think they are feeling like they should bet but are uncomfortable with their hand so are betting relative to the relative strength of their hand. I will be calling sometimes to attack turn bets that look similar.

Well, this is one of the worst run-outs for your hand and one that absolutely smashes villain's range. Since you're deep stack I'd probably still fire a flop bet but once I see the turn card I'm getting into check/call mode.

As played you obviously have to fold vs. raise.

As played turn should be an easy fold with almost everything beating you.

On that board though I would think that checking is better than betting. I'm torn on whether or not I would call a bet. It obviously depends on villain's range, but given how deep we are just about any player is crushing that board with a 4 bet calling range. We're probably overfolding from a theoretical standpoint if we do check fold but I'd still make my choice based on what villain plays like overall rather than worrying about being exploitable.

If you're IP I think you can check back some % of the time but I do think betting will be better. Though, if villain is OOP he should have a tighter range that might not include as many broadways that would his 1-pair hands or draws on this flop. AA is pretty far up in your range though since the only better hands are likely the few combos of QQ. AA is definitely not similar to a 2nd pair holding here. On turn both IP and OOP I'm slowing down since many hands improve in villain's range.

Best exploitative line is probably to reduce turn sizing significantly but still bet. Obviously a bad card, but that doesn't automatically mean that we want to give a bunch of free rivers. If we get raised it's a bet/fold of course.