At 1000bb: raise aces, call the nut-makers, and never forget their 3-bet was aimed at a steal.
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.
The big blind 3-bets your cutoff steal. The discount made their call cheap — the 3-bet means they chose not to take it.
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.