Suppose we have an object with weight = mg. How much will its gravitational potential energy change if we raise it to a height h?

As the object (here, a book) is raised a distance h from the floor, gravity does work = (Force)(distance) = mgh. Therefore, the energy stored by gravity  the gravitational potential energy = mgh 
Following the steps for calculating potential energy:
Example 1: A block of mass 2.0 kg rests on a table. If its gravitational potential energy is 0 Joules now, what will its gravitational potential energy be when it is raised 1.0 meter above the table?
Solution: m = 2.0 kg, h = 1.0 m, g = 10 m/s^{2}
GPE = mgh = (2.0 kg)(10 m/s^{2})(1.0 m) = 20 Joules
Solution: If GPE = 0 J at floor level, then mg = 8.0 N and h = 75 cm = 0.75 m
GPE = mgh = (8.0 N)(0.75 m) = 6.0 J