This is nothing to do with weight but the force of gravity, acting on the object. The gravitational force of the Moon acting directly above the object reduces the gravitational force of Earth a little.
Moon overhead and underfoot means that the moon is either straight up (overhead) or straight down (underfoot). These terms are heavily used in the hunting world to determine the activity of deer, as they tend to be more active when the moon is in these locations in the sky.
It is widely believed that deer are more active when the overhead and underfoot times are close to sunrise and sunset. Though many studies have been done regarding this theory, they are not currently backed by studies.
One of the first and most known writers regarding this topic is the late Jeff Murray, who studied for years how deer moved according to the phase and position of the moon and based on this information.
