Question

why is the weight of an object on the moon is one sixth its weight on the earth

Answer 1

the weight of an object on moon is one sixth its weight in Earth .this is because moon has gravity equal to 1/6 th of Earth

Answer 2

Because gravitational pull of moon is one-sixth of earth's gravitational pull.
As the doesn't changes anywhere, it is all because of gravitational force.
Thus we can say that it an object will be placed on earth it's weight will be different. And if the same object will be taken to mars it will weight different.