Let's assume our opponent is somewhat a standard reg for the sake of simplification and theory reasons.

We clearly have a very strong hand on the flop but it's not the strongest part of our 3betting range. I much rather prefer to have something like AJT9dd or AAQTdd instead. What's our line on the flop? Do we want to always bet this hand? If so, how do we proceed against a check-raise? I feel like the issue here is the SPR, even though that's a 3bet pot. Would we bet if we were 200bb as well?

I am not a big fan of my sizing now anymore, at the same time, once we are betting we are not folding so we might as well pot it to extract max value from draws and protect our hand?

Does checking have some merit to extract value on future streets as well as to protect our checking range?