This is going to be tough without reads but on a board that dry you should definitely expect villains to be check calling AA and QQ a decent amount. Once they elect not to c-bet, there's really not much need for them to raise the flop.

You should really have a plan for this hand before you bet the flop. You're rarely getting a fold on that flop for one half pot sized bet so betting once and giving up on the turn is likely lighting money on fire.

I don't feel great about it. We should probably check more often than we bet overall in this spot, villains range is somewhat strong, even when he checks.

I don't mind flatting pre 100bb deep IP any pair if blinds are rec, but in general I would play it just set mining (maybe barreling only in some boards with gutshot equity). If villain is a decent regular he's probably putting a lot of Ax in his checking range, also strong aces as AT or AJ when OOP and maybe even some traps.

When we think about which of our hands that can go 2 or 3 streets for value in such run out, we realize that villain has a huge range advantage. We pretty much rep only 66 and maybe AQ if we flat call it vs an MP open, which is debatable. Since we have so few nutted hands in this spot, our bluffing combos should also be only a few. If I'm bluffing in this spot I'd use hands such as JTs or KTs which have gutshot+BDFD equity and block some of villain's strong aces that might check flop.