Isaac Newton postulated the Law of Gravity approximately 340
years ago. He theorized that any two objects exert an attractive
force on each other. The magnitude of this attractive force is
directly proportional to the product of the masses of the two
objects and is inversely proportional to the square of the
distance between them. Thus, for objects with masses M and m
that are a distance D apart, the force F of attraction between
them, according to Newton is:

According to this
relationship, if the mass of one of the objects, M or m, were
doubled, then the force of attraction F would be doubled.
However, if the distance D between the objects were doubled, the
resultant force F would be ¼ of its prior value.

If the Earth is used as one of the masses (say M) and an object
on the surface of the Earth is the second object m, then the
force F can be considered the weight W of the object m.