Let the force exerted by Earth on an object of mass 'm' at height 'h' where the gravitational acceleration is 'g' be 'F' and the potential energy of the object be 'E'.
We know,
F = mg
(for a body experiencing gravitational pull of magnitude 'g')
And, E = mgh
Replacing mg = F in E, we get:
E = F x h
That is the relation between potential energy for a body at height 'h' and the gravitational force it experiences at that height.
