How is the Gravitational Force related to what we call weight ?
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.
Your "effective weight" can change, that is, if you are on a scale in an elevator which suddenly moves upward, the scale will suddenly read a different amount. This has to do with the motion of the elevator rather than a change in your mass or the force the Earth is exerting on you. Another example of this is the astronaut in space who is "weightless". The Earth is still exerting a force on the astronaut, but because the space craft is accelerating as well, the astronaut will appear "weightless".
How does one quantify the gravitational force ? The magnitude
of the force is mass * |gravitational acceleration|. On Earth,
the gravitational acceleration (often written as g) is 9.8 m/s2
On the Moon, this value is about 1.6 m/s2.
To review: GRAVITATIONAL FORCE