Never assume. That wasn’t part of the question. My reference point could be the Horsehead Nebula.
You can assume the orbit of the moon is perfect and the radius of the orbit is 238,857 miles cg to cg.
1) If you don’t specify a reference point, I get to do that.
2) Even if your reference point is the Horsehead Nebula, the weight of the Moon is still not zero. It may be smaller than your error bar, but it’s still not zero. Fg=G*Mm*Mhhn*R^-2