I am currently playing around with Coffee Calcs to figure out which hands I can include in my check-raise flop ranges in 3bet pots, both for value and bluff on dry boards.

So, for example we raise and get 3bet preflop. Board comes Jc 6h 3s and villain cbets 1/2 pot.

What hands should we be thinking of raising here? AJ, KJ, QJ? 45s?
What about middle pairs like 7h7c that are likely to be ahead of villains range and need protection?

If we suspect our opponent holds perhaps AK, AQ type hands, isn't flatting with a hand like 9c9s going to allow our opponents to barrel a ton of scary turn cards and denying us our equity?

Am I missing something with my logic? Help would be much appreciated.

It's true that hands like 99 might benefit from x/rs, but it's important to remember that sometimes we'll be piling money in vs hands that have us crushed and when we get flatted we're still going to have some ugly spots.

In general those hands don't tend to be x/red very much until we're shallow enough that they can play for stacks anyway.