Weight=mass x gravity.But as mass doesn't change anywhere in da universe,so on moon n on earth mass will b same.Weight depends on accelaration due 2 gravity 'g' and its value on earth is 9.8,on da moon it is g/6 approx..So,weight on moon is 1/6 times to weight on earth. So,astronaut weigh less on moon than earth.
Because the moon has no gravity but the Earth does so that proves that we would weigh less on the moon than the Earth.