When holding Aces on a paired board in a 3-bet pot, prioritize checking back to protect your range and induce bluffs rather than overplaying against a range that contains all the trips.
Checking back is the preferred play here. While we have an overpair, the paired King board heavily favors the 3-bettor's range, and checking protects our entire range while keeping Villain's bluffs in.
Note: Betting here is a slight mistake; checking back Aces on this texture is higher EV as it protects your checking range and prevents you from getting check-raised off your equity by trips.
After being check-raised, we should simply call. Shoving is unnecessary as it only gets called by hands that beat us (Kx, 44) and folds out the bluffs we want Villain to keep firing on the turn.
Note: Shoving over the check-raise is an overplay; calling allows Villain to continue bluffing with hands like QJ or pocket pairs that we dominate.