weight
Weight is how hard gravity pulls on an object. It is what a scale reads and what you feel in your legs when you stand. Unlike mass, weight depends on where you are: the same person weighs less on the Moon because the Moon's gravity is weaker.
Weight is a force, a vector pointing downward toward the center of the Earth, equal to the object's mass times the local acceleration due to gravity: W = m g. Near Earth's surface g is about 9.8 m/s^2, so a 1 kg mass weighs about 9.8 N. The SI unit of weight is the newton (N), the same as any force, not the kilogram.
Because g varies, weight varies: on the Moon g is about 1.6 m/s^2, so weight is roughly one-sixth of its Earth value while mass is unchanged. What a scale actually measures is the support (normal) force it pushes up with; in free fall or orbit that support vanishes and you feel weightless, even though gravity, and your mass, are still there.
A 60 kg student weighs W = 60 times 9.8 = 588 N on Earth, but only about 60 times 1.6 = 96 N on the Moon. Their mass is 60 kg in both places.
Weight = mass times g, so weaker gravity means less weight.
In everyday speech we 'weigh in kilograms', but strictly kilograms are mass and newtons are weight. Weightlessness in orbit does not mean gravity is absent; the astronaut and station are simply falling together.