What do you mean by weight of an object on the moon ? Why is the weight of an object on the moon is less than that on the earth?
The force with which the object is attracted towards the centre of the moon is the weight of an object on the moon.
The mass and radius of the moon is less than that of the earth. Due to this the moon exerts lesser force of attraction on the object. Hence, the weight of an object on the moon is less than that on the earth.
The gravitational force of the moon is about one sixth of that on the earth.
Example. Suppose the weight of a certain object is 6 kg-wt on the earth. If the same object is weighed on the moon, then the weight will be just 1 kg-wt.