Gravitational field strength, g, is the force on each kilogram of mass. It is measured in N/kg and is different on different planets and moons. On Earth g is 10 N/kg, on the Moon about 1.6 N/kg, and on Jupiter about 25 N/kg.
The weight of a body is directly proportional to the gravitational field strength where it is. For a fixed mass, if g doubles then the weight doubles. A graph of weight against mass is a straight line through the origin, and its gradient is g.
Mass does not change, so the same body has a different weight in a different place. A 10 kg object weighs 100 N on Earth, 16 N on the Moon, and about 250 N on Jupiter. The weight is smaller on the Moon because g is smaller, and larger on Jupiter because g is larger. To find the weight in a new place, work out the mass from the weight on Earth, then multiply by the new value of g.