Question

Which pulls harder gravitationally, the earth on the moon, or the moon on the earth? which accelerates more?

Answer 1

the earth the earth pulls the moon tuords it the earth has more mass and the reason why the moon does not just crash into the moon is

Answer 2

Gravitational forces are always equal in both directions. So the moon accelerates more because its mass is smaller than the Earth's mass.

Your weight on the Earth is equal to the Earth's weight on you. But when you fall, your acceleration down is greater than the Earth's acceleration up, because your mass is less than the Earth's mass.