Blind battle I assumed his range would be TT+, AQ+ based on table history and 3betting stat against BB and fold to 4bet in the same position:

PokerStars - €0.02 NL (6 max) - Holdem - 4 players
Hand converted by PokerTracker 4
Hero (SB): 137 BB
BB: 50 BB (VPIP: 11.06, PFR: 10.15, 3Bet Preflop: 6.34, Hands: 1,072)
CO: 120.5 BB (VPIP: 11.11, PFR: 5.56, 3Bet Preflop: 14.29, Hands: 20)
BTN: 103.5 BB (VPIP: 24.61, PFR: 19.77, 3Bet Preflop: 6.95, Hands: 1,826)
Hero posts SB 0.5 BB, BB posts BB 1 BB
Pre Flop: (pot: 1.5 BB) Hero has Q♥ Q♦
fold, fold, Hero raises to 3 BB, BB raises to 8 BB, Hero raises to 137 BB and is all-in, BB calls 42 BB and is all-in
Flop: (100 BB, 2 players) 5♦ Q♣ T♣
Turn: (100 BB, 2 players) J♦
River: (100 BB, 2 players) 6♦
Spoiler
Hero shows Q♥ Q♦ (Three of a Kind, Queens)
(Pre 17%, Flop 88%, Turn 77%)
BB shows K♥ K♦ (One Pair, Kings)
(Pre 83%, Flop 12%, Turn 23%)
Hero wins 96 BB