I normally don't do this, but since you're playing a fast-fold format I think you'll benefit from the GTO solution. If you think that the GTO solved lines are too far away from optimal given your player pool disregard this entire post.
I've run the hand through a solver, allowing 33% 66% and 75% bet sizings on the flop with a standard sizing of 66% solved to 1% dEV.
Pre flop range for CO was set to:
AA-44,AKs-A2s,KQs-K4s,QJs-Q6s,JTs-J7s,T9s-T8s,98s,AKo-A8o,KQo-KTo,QJo-QTo,JTo,[50.0]33-22,K3s,Q5s,97s,87s,A5o[/50.0]
Pre flop range for BB call vs CO RFI was set to:
99-22,AJs-A6s,A2s,KQs-K4s,QJs-Q8s,Q5s,JTs-J8s,T9s-T7s,98s-96s,87s-86s,76s-75s,65s-64s,54s-53s,43s,AQo-ATo,KJo-KTo,[50.0]A3s,K3s-K2s,Q7s-Q6s,Q4s,85s,63s,A9o,KQo,QJo-QTo,JTo[/50.0]
Flop:
BB checks to the pre-flop raiser at a near 100% frequency (probably only donking sometimes because I didn't solve to a small enough dEV). On a two-tone, connected broadway flop it's very common for the RFI to choose a larger c-bet sizing (GTO+ bets 66% and 75% for 50% of its range, checks back 50% and never uses the 33% sizing). Some people would standard c-bet this flop at a 100% frequency with the 33% sizing because it's supposed to connect better with RFI's range, but you're actually supposed to check most of your marginal made hands and some junk. Overpairs are bet at a 100% frequency using a large sizing though (so on the flop you made the GTO play).
BB is supposed to call that bet with most made hands (only raising sets, some two pair combos and balancing the raising range with flush draws and OESD). Weak pairs and junk are mostly folded.
Turn:
Given the flop action and now the OOP check you're supposed to check back all 6 combo's of AA. As the pre-flop raiser with the betting lead you're playing an uncapped range against a capped range. With the flop action, the calling player holds the range advantage more often than not though (because the pre-flop raiser can c-bet a larger % of his range compared to BB's calling range). That's the fundamental reason we're checking back the turn at a higher frequency than the flop. BB is also representing a strong enough range that value-betting AA is not really worth it.
KK being the only other overpair is bet at a 100% frequency as you're also drawing to a straight with that combo (so if we get check-raised we're comfortable calling with KK). Getting check-raised with AA is a different story though. If I set AA to bet the turn the solver folds all combo's of AA as it assumes a BB check/raising range to consist only of made straights balanced with flush draws. I think for your game and player pool the average check/raising range is even more skewed towards only containing straights. Given the action folding, AA and maybe over-folding KK as an exploitative adjustment feels best. EDIT: Probably not folding KK as you hold blockers to the nut straight
Because getting check-raised with this overpair (AA is still in a good spot against BB range) is a nightmare, we're checking back the AA for the purposes of pot control and
equity realisation. The plan here is to check back the river on any card and call when facing a bet most of the time (only folding against a bet on river cards that give four to the straight, complete the spade draw, or high cards that pair the board).
Key conclusions for playing overpairs on this texture:
- c-bet larger at a lower frequency (you already do this)
- Check back overpairs on the turn if draws complete for equity realisation and pot control unless you have a reason not to
- Call river bets on most river cards
- Call river bets on completed flush draws for which you hold the flush blocker