[Catt]

You're making a lot of assumptions here. You gave no read, so I'm treating him as unknown. You have 44 which means that if he's C/Ring a worse hand, it is total air or some draw. Do people do this at 10/20? Sure; but those sorts of people aren't usually the kind that open-complete in the SB HU and then ck-cl the innocuous flop against a BB's auto-bet after BB's PFR. Your hand is very vulnerable but may be best. If it is best he almost certainly has at least 6 and maybe upwards of 15 to improve. I think if you're C/Red on the turn, you can let it go and feel fine, even if this time it was a worse hand. You need a reason to believe this guy is capable of C/Ring a worse hand with enough frequency to either call a C/R (with little chance to improve) or check through with such a vulnerable hand. You also need a reason to believe he'll bet the river after you check the turn. I know the game is aggressive, but there are plenty of guys who will check to you on the river, too, planning on calling sometimes, folding sometimes, and raising sometimes. And as Fianchetto said, plenty of guys in this game will peel the flop and fold the turn for a bet. Unless you have a reason to suspect he's capable of C/Ring air I think you should approach this pretty straightforwardly - which is to bet the turn and fold to a raise.

I'd save this sort of play with a made hand with little chance of improving on the river for when you're up against a player that you know is aggressive and tenacious in blind-vs-blind situations.