The weight of an object is the force of gravity pulling on it. It is found with W = m × g, where W is the weight in newtons (N), m is the mass in kilograms (kg) and g is the gravitational field strength in newtons per kilogram (N/kg).
The value of g depends on the body you are standing on. On the surface of the Earth g is about 10 N/kg. On the Moon it is about 1.6 N/kg, because the Moon has much less mass than the Earth, so it pulls less strongly on everything near its surface. The value of g depends on both the mass and the radius of the body. For the Moon and for Jupiter, the difference from the Earth's g comes mainly from the difference in mass, so Jupiter's g of about 25 N/kg is greater than the Earth's. The radius matters too: the further you are from the centre of a body, the weaker its pull.
Mass is the amount of matter in an object and does not change from place to place. Weight does change, because g changes. A 60 kg astronaut has a weight of 600 N on the Earth but only 96 N on the Moon, yet is still 60 kg in both places.