SCs/one-gappers are a frequency thing for me, I'm not actually as wide as 100% J9s here. I'll call it quite occasionally but more often if I'd like a pot to go multiway with one of the players in the blinds (note BB <100bb stack ;)).

This is a flop situation which I don't understand at all. I'm still struggling to learn how to play against players with balanced c/f-c/c-c/r frequencies. Here's my GUESS at what I'm meant to do here.

I think I want some sort of range largely intended for protection betting. The board is just way too wet for me to want to let free cards come with my hands like JJ-99 and that creates an incentive for me to have this range and bet somewhat small with it. The point of betting smaller is to lose less to UTG's c/r's. I also wonder if betting smaller makes it harder for him to balance his c/f-c/c-c/r frequencies since when he checked it would have been with a range of hands already intended to go into certain different ranges but a bet this small might change where they want to be which could lead to him doing awkward things like c/c'ing hands which planned to c/f or c/r'ing hands which planned to c/c and when he does this with hands which don't want to do it very much it should hurt his ev.

I think I also want a more standard range intended for value betting and bluffing. While this will look more like a polarized range I probably need to be careful (GTO-wise) to put a few of my nutted hands in my other range as well. While I'll make less value with the nutted hands by getting called I am pretty sure there is an equilibrium where my smaller range has fewer nutted hands so it gets played back at more so the nutted hands in it make more money etc. such that I end up wanting maybe 20% of my nutted hands there and 80% in the bigger range (this is complete guesswork, I can't back that number up mathematically).

I feel like a perfect GTO model would have balanced ranges for every reasonable betsize here and it would make villain's life absolute hell. Like given how hard it is to balance checking ranges and work out how to defend 1-A and work out some hands are best as c/r's imagine how hard it must be if you're completely in the dark on how large the betsize of the IP player is going to be. I know that this will hurt IP immediate strategy on the flop, like there are some betsizes which make more sense than others on the flop, but completely hamstringing OOP's ranges all the time seems like it would make up for flop losses on the turn. Rather than doing that perfectly I wonder if I could just randomize my betsize with this nutted range somewhat.

I also feel like maybe I'm completely wrong though. Would love to hear if there's a standard opinion on this.

I feel like this betsize is possibly bad because OOP can have 98s here. I think after the flop c/c it's really hard for him to have anything better than that though so I like having a polarized range betting quite large in this spot, it's easy for me to create one for myself since I have more nutted hands than him from the flop and then I have 98s too!

River merges our ranges quite a lot because we can be bluffing with aces and OOP can maybe have gotten here with an ace too and the smaller betsize relative to the pot compared to the turn reflects that. Overall though I think we were bluffing with an ace enough that we have enough value hands to support following through with at least the JT J9 T9 bluffs.

Let me know if this stuff seems really bad, I'm still trying to get a good grasp on betsizes and especially IP vs a check from the pfr it seems like there's a TON of room to be creative.