I assume you are in position (is villain btn?).
I like the flat preflop based on the logic that he's folding all of his range to our 4b. Plus, stacks are short enough that we can risk it with the capped implied odds.

Does he have any history of him 3betting us? Will he do this OOP with AJ+, 22+? Is he going to cbet 100%? Any idea how he plays 22-QQ when flop is AXX?

If he is reraise folding JJ 100bb deep, 4 bet the hell out of him with anything.

Is he 3betting polarized or merged?

If you play with the same players a lot and you are trying to balance ranges then I like a call, but if you know you will never see these players again then I like to just play it straightforward and 4-bet here.

We need positions and stack sizes, otherwise it's hard to say anything.

You consider him a good player and he folds JJ/AQ to a 4bet, maybe even AK/QQ? Probably not that great of a player...

If he really does fold those strong hands to 4bet, I like just calling the 3bet. We keep his range wider, we don't get 5betted and our hand strenght is disguised.

If flop comes Axx, I would usually just play for 1 street and not put any more money in. If villain cbets, I would call once and fold the turn. If flop/turn goes check/check, I would valuebet etc.