Why does an object have a different weight o the moon than it does on earth

The gravity on the moon is different than on earth.

Our weight on moon is less than it would be on Earth due to a difference of the strength of gravity on the moon. The moon's gravitation force is determined by the mass and the size of the moon. Since the moon has significantly less mass than the Earth, it will not pull objects toward itself at the strength that Earth will. This means that if you went to the moon you would weigh less, even though your mass stays the same.