AA batteries have about 4 watt-hours (14400 joules, 10620.9 pound-feet).
Ignoring losses, does that mean a AA battery could theoretically lift 10,620.9 pounds, 1 foot high?
You'd need an electric motor, some sort of crane or lift, the right gearing, and a fair amount of time. What's the best efficiency you could hope for? Even with 50% loss, you should still be able to lift a pickup truck, but this feels wrong (impossible).