Standard spot, let's experiment

$2/$5 in a $500 cap game at Borgata

Hero has solidish image (by my standards), some unusual backstory worth mentioning. There's this one reg in the game who is absolutely terrified of me, and has probably unique opinions about my play. He thinks I'm really super tight and rarely bluff and I always show up with the nuts. Now, it is probably true that I am tighter than my normal persona/image/appearance suggests, but it is nowhere to the extent that this guy thinks. Part of it is he's a nit, smalk sample size, part of it is he has been able to make ridiculous hero folds against me by making correct reads. Anyway, he's expressed this opinion very loudly at this table many times, and asked for a transfer.

Also, I lost a huge 3-way pot that was all in on the turn with the stone cold nuts. Obviously this didn't do anything to change my game, I've played great since then. There was also an unusual hand at one point where I bet flop, turn went c/c, and I called a river bet from a maniac, who just quickly mucked, I informed him I called with Ace high.

Anyway, consider this standard, not really interesting hand:

Game is now 6-handed, very bad older fishy gentleman limps CO and has $350, I have $600 and raise BTN to $20 with A9ss. Raise size is a little on small side because of several factors: CO's stack size, I'm on the BTN, the game is shorthanded and I'm going to be opening quite a bit wider. SB folds, BB calls and CO calls.

BB has $550 and is an early 30s white guy, nondescript, probably just tries to play TAG and not leak money, pretty common for bad regs in this game.

Flop ($62): Ad 2c 6c
BB checks, CO checks, Hero bets $35, both call.

Turn ($167): 7s
BB checks, CO checks, Hero?

This is pretty clearly a value bet but it's arguably a little thin. Even shorthanded, BB is not calling with many bad off suit Ax IMO, he'd probably 3-bet AK but maybe not AT-AQ. CO has a flush draw or some midpair he's stubborn with.

What's your estimate on our equity here? Probably in the 40%-45% range vs. 2. What should we bet here? Probably $80-$120, and I lean toward the smaller side to make sure we aren't folding out the BB's worse hands.

Now, what if we did this instead.

Flop ($62): Ad 2c 6c
BB checks, CO checks, Hero checks.

Turn ($182): 7s
BB bets $35, CO calls, Hero raises to $125.