Why is the weight of an object on earth different from its weight on the moon is?

There are many differencese between the moon and earth. The biggest difference is that the moon has very low gravity. If you were on the moon, you would weigh 1/6 of what you weigh on earth. The reason the moon has such low gravity is because the moon has a very small mass. Mass affects gravity. To learn more about this, see Einstein's General Relativity. Because the moon has such low gavity, an atmosphere can't exist on the moon because there's nothing keeping it in place around the moon. Because there's no atmosphere, there is no erosion. That's why the moon is cratered, because about 4.4 billion years ago when the solar system was just forming, the moon got hit a lot by asteroids and smaller planets that don't exist anymore. Because there's no atmosphere, there's also no air friction, so if you drop a rock and a feather on the moon, they would fall at the same speed. There are many more differences, but you're probably getting bored by now. I hope this helped.