Top of my range facing river shove

Posted 7 years, 3 months ago

Blinds: $0.01/$0.02 (6 Players) BN: $2.04 (Hero)
SB: $2.15
BB: $3.33
UTG: $5.25
MP: $3.89
CO: $2.06

Preflop ($0.03) Hero is BN with A A

3 folds, Hero raises to $0.04, SB folds, BB raises to $0.14, Hero raises to $0.38, BB calls $0.24

Flop ($0.77) Q 3 Q

BB checks, Hero checks

Turn ($0.77) Q 3 Q 4

BB checks, Hero bets $0.42, BB calls $0.42

River ($1.61) Q 3 Q 4 2

BB bets $1.24, Hero

On the river I have the absolute top of my range. Can we ever fold here?