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If the moon were just a rock on our lovely little planet, it would (supposedly) weigh about 73-81 billion tons (so anywhere between 146,000,000,000 and 162,000,000,000 pounds).
However, the moon is moving through space in free-fall and is therefore regarded as weightless.
My guess is that you are actually looking for the mass of the moon. http://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html
"The weight of the moon is 0. This is because moon is continuosly falling into the Earth due to the gravitational attraction of the Earth and is held in its circular path only because of its tangential outward force(Shortly, it is held in its orbit due to Centripetal force). However, it has a mass and it's mass is estimated to be 7.347 * 10^22 kg.
Undoubtedly, you would remember that weight of a freely falling body is 0. Hope this is a good enough answer for you"