What do you understand by the gravitational force of earth and weight?

Weight:The force that gravitation exerts upon a body, equal to the mass of the body times the local acceleration of gravity: commonly taken, in a region of constant gravitational acceleration, as a measure of mass.

Any object on the Earth or at least close to Earth, will experience a gravitational force. For example, when one shoots a basketball, the force of gravity acts to pull the ball back to the floor.

Gravitational Force is related weight as follows: The gravitational force on Earth is equal to the force the Earth exerts on you. At rest, on or near the surface of the Earth, the gravitational force equals your weight. On a different astronomical body like Venus or the Moon, the acceleration of gravity is different than on Earth, so if you were to stand on a scale, it would show you that you weigh a different amount than on Earth. 

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