Why does earth have more gravitation pull than the moon

I'm not that good at this: but I believe it is because the moon has less mass.

This is because gravitational force is directly proportional to the mass of an object. Greater the mass, greater will be the gravitational force exerted by it and thus, more will be our weight. As the moon has lesser mass than the earth, it has a weaker gravitational pull and hence, we weigh less on the moon.