Weight is the force acting on an object due to gravity. Close to the Earth this force comes from the gravitational field around the Earth. Because weight is a force it is measured in newtons (N), using a calibrated spring balance called a newtonmeter. The weight of an object can be thought of as acting at one point, called its centre of mass.
The weight of an object depends on the gravitational field strength, g, at the point where the object is. Weight is calculated with W = m g, where weight W is in newtons, mass m is in kilograms, and g is in newtons per kilogram (N/kg). In a calculation the value of g will be given. For example, a 5 kg object where g is 10 N/kg has a weight of 5 × 10 = 50 N.
Mass is the amount of matter in an object, measured in kilograms, and it never changes from place to place. Weight does change. On the Moon g is about 1.6 N/kg, so the same 5 kg object weighs 8 N there.
Weight and mass are directly proportional (W ∝ m), so doubling the mass doubles the weight when g stays the same.