When to 3-bet or just flat call

Typically, when I'm in early position with AA-JJ and the previous player bets large, I tend just 3-bet in order to knock out the following players from getting a good price to come in. At what point, based on how many players are left playing, should I flat call?

based on your play
you should mix both 3bet and flat calls, so they can't read you easily

Generally you should be 3-betting these hands. This is particularly true if stacks are good for shove-fold. For example, if UTG raises to 4bb and you have QQ with a 20bb stack, just move all-in and expect to get called a lot (since he's showing strength by putting in a big raise from early position).

The main time to just call is when you have a maniac left to act behind you and want to keep them in.

In cash games it is all about building your 3-bet range. Sometimes, it is good to have bluffs in your range (especially with Ace and King blockers) against opponents who are capable of folding. Sometimes, especially against fish it is better to just play a linear range and 3-bet only for value.