Objects Weigh Slightly Less When the Moon is Directly Overhead
Every mass in this universe attracts every other mass by a force proportional to their masses and inversely proportional to the square of the distance between their centre of masses - this is gravitational force.
Gravitational Force and Weight
A person standing on the surface of the Earth experiences a huge force due to gravity of the Earth, which has an enormous mass (5.972 × 1024 kg) and close proximity (merely 6370 km). And this force acts directly “down” i.e. towards the centre of the Earth (ignoring variations of density for this discussion). Coming to the moon, it is relatively smaller in mass (7.348 × 1022 kg) and at a huge distance (384,400 km) from the person standing on the Earth’s surface. Therefore, the moon exerts a tiny force on this person (towards the centre of the Moon) compared to the huge force exerted by the Earth. So, when the Moon is directly above you, the gravitational force of the Moon acts “upwards” (in the directly opposite direction to the gravitational force of the Earth acting downwards). It effectively pulls you away from Earth’s centre, hence making your weight least among all other positions of the Moon.
Findings
Though the gravitational force due to the Moon on a person is miniscule (about 0.5g for a 50kg person), it is still measurable. In fact, you wouldn't see any difference on your bathroom scale. The variation would be trivial - like the difference between inhaling and exhaling. If you want an exact estimate of how much less you'd weigh, consider this estimate: Your weight would change by less than one-millionth of its total amount.
