The densities do vary by almost a factor of 2 (~3 g/cc for the Moon, 5.5 g/cc for the Earth), but the larger problem is that surface gravity is a linear functio

The densities do vary by almost a factor of 2 (~3 g/cc for the Moon, 5.5 g/cc for the Earth), but the larger problem is that surface gravity is a linear function of the radius, and mass is the cube of the radius. Consequently, the mass of an object with a given surface gravity is inversely proportional to the square of the density. If the Moon were the same density as the Earth, and had the same surface gravity as it does now, it'd actually mass less than it does now -- and Uranus, despite have 15x the mass of Earth, has a lower surface gravity, because its density is so low. The rule of thumb for space is "any way your intuition can be wrong, it will be wrong". :-)