What is gravity? how does it affect weight?

Gravity

the force that attracts a body toward the center of the earth, or toward any other physical body having mass. For most purposes Newton's laws of gravity apply, with minor modifications to take the general theory of relativity into account.

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.