Why would you weigh less on the Moon than you do on Earth?
The reason that you would weigh less on the moon is that the moon's gravitational force is less than that of Earth. The law of gravity dictates that all bodies of matter attract each other with a force proportional to their mass. The moon's mass is only about 1/6 that of Earth, so gravity's pull is proportionally weaker as a result.
Note that your mass would not change, only your weight, which is purely a function of the force of gravity. If you were to run into a wall on the moon, it would be no different than hitting the same wall on earth, as your mass (and therefore inertia) still result in the same force of impact.