Weight and Mass

$W = 50 \times 10 = 500 \text{ N}$

$W = 50 \times 1.6 = 80 \text{ N}$

Her mass remains 50 kg anywhere.

Airlines set a maximum mass (e.g. 23 kg) for checked luggage — not a maximum weight in Newtons. Baggage scales measure the gravitational force on the bag and divide by $g$ to display the mass. A 23 kg suitcase weighs $W = 23 \times 10 = 230$ N on Earth, but you'd only need to lift 37 N of force to move the same suitcase on the Moon.

An astronaut has a mass of 80 kg. On Earth she weighs $W = 80 \times 10 = 800$ N. On the Moon ($g = 1.6$ N/kg) she weighs only $W = 80 \times 1.6 = 128$ N — about a sixth of her Earth weight. Her mass stays 80 kg wherever she goes; only the gravitational force (weight) changes with location. This is why astronauts can leap several metres high on the Moon.

A spring scale (like a bathroom scale) measures weight — it records the gravitational force pulling you down and converts it to a mass reading using $g$. If you used the same spring scale on the Moon, it would show a wrong (lower) mass. A balance scale compares your mass against known masses; because gravity acts equally on both sides, it gives the correct mass reading anywhere in the universe.