Ok when 3-bet then called get called in 2 different spots I'm pretty happy id associate a fairly middle strength range to both. Id also include AK in the original raisers range as a player pool tendency many are passive OOP with AK.

On this flop i feel that when i check it allows anyone to bet and make me fold, and i wondered if i should cbet so that my c betting range isn't so obvious. I would have virtually no draws.

If i bet QQ it wouldn't be for value or as a semi bluff so i feel i should check in this spot but it then turns my hand transparent. Should i check some AK/KK/AA here too in order to protect my check back range or shall i just accept defeat and not think twice about flop check?

Just a thought that sprang to mind