Gravitational potential energy is stored between any two objects. So, for every object on or near Earth, there is gravitational potential energy stored between the object and Earth.

The amount of gravitational potential energy stored between an object and Earth depends on the mass of the object. The amount of gravitational potential energy also depends on the distance between the object and the center of Earth. This distance increases when the object moves higher and decreases when the object moves lower.

If the distance between an object and the center of Earth changes, the gravitational potential energy stored between the object and Earth will change.

When an object's mass stays the same and its distance from the center of Earth:

increases... it's gravitational potential energy stored between the object and Earth... increases

decreases... it's gravitational potential energy stored between the object and Earth... decreases

stays the same... it's gravitational potential energy stored between the object and Earth... stays the same