I think the reason some people might believe this claim is because we’re taught in school that the moon’s gravity causes the tides. I think the reasoning goes, “well if the moon’s gravity can affect the tides, surely it can affect smaller things too”
First of all, the amount of water in your body doesn’t matter. Gravity doesn’t just affect water.
Secondly, the gravity of the moon on earth is about 1/10 millionth of the gravity of earth itself. So basically you lose more weight by spitting once than you lose because of the moons gravity.
And thirdly, why only during full moon? The moon is still there even when it’s not full, so the gravity is also still there. Even during the day the moon is still there.
All this full moon stuff is just pseudoscience.