how gravity is related to the weight of an object

An object with twice as much mass will exert twice as much gravitational pull on other objects. The gravitational force increases as the size of an object increases. On the other hand, the strength of gravity is inversely related to the square of the distance between two objects.

Gravity is related to a weight of an object because when you drop a 500 page book and an apple at the same time the book will land first.