Why would it be standard to bet here, and what would be the reasoning for a bet?

Reasons to bet would be, your hand is vulnerable to a large part of his range here J10,JQ,JK,KQ,K10,Q10 etc and you need to protect it.

Reasons to check are that, really, not many hands you beat are going to call maybe 77, 8x and club draws. But if he calls then you are not going to know what to do on river if you don't improve.

I probably check and let him stab again with his air. A lot of regs to check back weak aces on boards.

I prefer a x/c OTT. If you bet and get called you have no idea what to do on a low river card.

I don't even know if X/Cing the turn is that great. It would be interresting to know if he cbets his air on this flop IP (hands like T7cc, KQcc...). If he does, it's not a great spot as I don't think he is betting worse OTT in his Xb value range (hands like 8x, 4x, 77/55 OTT).

So the standard is to X/C but if vilain is a high cbettor it's not that great and we will have a difficult decision if he barrels the river, especially on clubs, 7, 5 (maybe some OC too)

When he checks back flop he almost always has 22, 33, 55, 8x, 99-KK, A2s, A3s, A5s, A7s, some slowplays and some small % of suited/off suit broadways i.e KTs-KQs + JTo-KQo, that either have sdv and pick up more equity on the turn or are flop give ups and are barreling some % of turns.

Expect him to cb all good hh, dd, cc suited connectors and broadways with good barreling equity so your betting/checking range here should be pretty easy to construct.
Nines are a pretty easy x/f here.

*villain is good reg, *
So we have to discuss our entire ranges rather than against a fish that we can just say "he always has worse be 100% super exploitable in a common spot" .

standard to bet here?
What does your SB range look like? I wouldn't ever be in this spot since I'd be more inclined to have a 3b/fold range here.

If villain will cbet TT+/A2 in this spot I will check back turn.
If villain does not cbet TT+/A2 in this spot I will lead turn.

He's cbetting 66%. . on a dry A-high board in LP vs blind positions the only reason people at these stakes don't cbet is they have some sort of weak SD value. You just need to decide how weak is that SD value.

How many Ax do you have in your range in this spot? If he bets flop I think his Ax range > your Ax range.

Let's say he never checks AT-AK, well then all of a sudden, your value range >his value range OTT.

If don't want to be going so thin that you're not sure if you're trying to :
- Get thin value from underpair
- Foldout A2/TT-KK

Checking makes your life easier. Taking more descriptive notes in common spots makes this play easier. ~~ :)

I'd just check - I don't see a reason to bet here - his XB range might also include hands that crush you + we don't expect to get 2 streets + we don't need a lot of protection on Ahi flop + he might stab his air or go for a small protection bet with worse hands occasionally.