Something I often struggle with is when I'm out of position and hit the flop, but not in an ideal way. For example, playing a 6-max NL2 game in the small blind, I called a 3BB raise of the cutoff with QTs (the rest folded). Flop came AQ4 rainbow. Since I had middle pair, I only checked and he raised. Since the cutoff probably opens quite wide, I figured I had quite some equity against his range (later I checked in equilab and my equity was estimated to be 51,5%). Also a continuation bet is so standard that it didn't convince me he had an ace, so I called.
I'm not sure if this was the correct play. By not raising myself I'm showing some weakness. On the other hand, checking protects my checking range (though maybe I shouldn't be concerned with that at those stakes?). Or should I have folded to his bet because he could have an ace?
Turn was a Jack, so I was in quite a similar situation (though equilab says my equity dropped). I raised, trying to show strength. Looking back at this decision I think I should have checked again? If he had a jack my bet could have added value, but maybe that's a to small part of his range? In any case he called.
River was a four, we both check and he turns over an ace.
I've been in situations similar to this one quite often, so what should one do here? Check-call on the flop and check-fold on the turn? or check-call both? I think what makes this so hard is that continuation bets are so standard that they don't really give you any information on the villains range. Or am I missing something here?