At 1000bb the button calls with almost its entire continue range — including kings. Position converts patience into profit.
4-bet almost nothing but aces. Even KK often prefers a call — building a 1000bb pot preflop with one pair is a strategy of despair.
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.