Every pair and most suited hands peel — 200bb in position against a blind's 3-bet is the definition of implied odds.
AK begins migrating from 4-bet to call — stacking off 200bb with one-pair hands is no longer automatic.
You opened the button wide; the small blind 3-bet, as they should. You hold position and the wider range — both matter.
Assumes a standard 3-bet; 4-bet to ~2.2–2.5x the 3-bet. Deep, favor calls over 4-bets — a 4-bet pot at 500bb+ commits you with range disadvantage.