You made some very good points throughout your analysis. Checking behind and letting villain showdown a low pair - i hate when i do that. Even when i do incorporate checking with overpairs, if i check the flop i do get called down with low pairs quite often, on boards much worse than this with for low pairs, just because villain saw me check the flop

you found a good preflop +EV play and you don't want to give that EV back postflop by overplaying your hand or bluffing incorrectly. 

Ye, as soon as that river comes down villain is check/folding almost always.

I think you spot on with checking back the flop, the turn play is most interesting as we expecting villain to lead. So now it seems he is trying to showdown his AQ/AJ/AT/worse high cards - which is bad since we rep AK pretty hard. 

The nice thing about the turn is that you pick up outs to chop as well as picking up the nut flush draw, you only worried about facing a turn check/raise which you would have to fold to, which would be gross. 

It seems like villain wasn't interested in stabbing the turn. i wonder what other rivers you can bet on, besides clubs of course. It looks like villain wasn't thinking much and just trying to showdown worse. 

Against the range we likely up against better Ax/22-44 we chop/suck out 26%-30% of the time roughly.

One thing to consider is the possibility of getting bluff raised on the river in this spot in the future for betting your Ax bluffs. I actually kinda like betting really small on this river, because its so hard for him to call, and it might induce a bluff raise especially considering he likely doesnt ever expect us to have clubs.

I think from a gto perspective if you decide to 'always' bet your overpairs on that flop then you should also be betting worse. With your hand you have a lot of back door outs yoy can double barrel so I think cbetting isn't going to be terrible. Without balancing your floop betting range it means villains can fold all their range that isnt beating yours and call when it is since you sorta flipping your cards over.

Im no expert in balanced ranged but I think its wrong to say you ALWAYS bet when you have it and check whenyou don't

Do you check back sets and big pp on the flop? I think triple barreling here is good. It's extremely hard for him to continue with big cards, so just make him fold his equity. Once you miss cb on flop, you should definitely bet turn with nfd. He has shown a lot of weakness by checking twice, so why arent you betting for fold equity/value. I like toothpaste's idea to bet small on river. If you were in villians shoes, what would you need to have to call the river bet? 

I think it is an OK bet on the turn as we picked up more outs against villians hand. 

From a GTO perspective, it is bet as well. As we 3 bet some suited 9T, 89 preflop(i do), and would check back this flop for pot control. We dont rep a lot of over pairs, but I think we can just bet twice with our actual hand to balance out with the times we have 9T, 89s.

not sure about betting any river after a turn stab...playin a XC-line on this board structure after beeing 3b (and playin UTG/OOP obv) makes villain not very weak at all....so i expect still decent OP´s in his range that could herocall a lot of rivers...K is pretty optimal of course for heros range to shoot again, regardless of the flush

"I think 3-betting A3s here will be immediately profitable pre-flop and is an easy fold if I get 4-bet."

guys on nl100 for normal reg how big is his UTG 4BET bluff range?but i think you can shove again 4bet some percent of time with A2s-A5s