Pre-flop is good. It would be too thin to 4-bet for value without a read and folding is of course out of the question.

The flop stab is only good if SB certainly check/folds AK, which is not at all certain. His range should contain some AK, TT/99, Jx and maybe 98s type hands that will check/call. You still have showdown value also against the occasional give-up, so I would prefer to start with a check. (You can always bluff later to fold out AK if you want to).

Once you do bet and get called, you don't have any good barreling opportunities either. The best card would be a Q, but it will be hard to get much value there. On a T you get a good draw but now villain isn't folding AK or 99, and TT made a set. On a 9 he's not folding TT, and 99 made a set. (Jx doesn't fold any turn).

So I think your hand is a bit too strong to stab the flop, and would prefer to stab with a weaker hand that has more barreling opportunities (or a draw). You're not giving up on the hand just because you check back.

What is our range for calling a 3bet in this position?

You need to either empty the clip, or xb otf.
Firing once is bad, villain rarely xFolds right away I think. He has a lot of Jx, 99-TT type hands that are xC. He might xC AK.

Most of those hands cant take the heat though, so I'd fire at least twice and possibly 3 times. Villains range for calling down should be JJ and maybe 1-2 combos of AA, which is fairly narrow..