Weight, Mass & Gravity
The gravitational force acts between all objects that have mass. You only significantly notice them when one of the masses is very big, eg the Earth. All masses on Earth are attracted to the Earth due to its gravitational feild, which is 9.81 m/s^2.
Weight & Mass
A key point to get across is that weight and mass are not the same things, mass is just the amount of 'stuff' that an object is made up of.
Weight is the force that is acting on an object due to gravity. This force is caused by gravitational fields and the size of the force depends on the mass of the object and the strength of the gravitational field that the object is in.
Weight is directly proportional to mass and gravitational feild strength, so if the mass doubled, the weight would double and if the gravitational feild strength increased then the weight would increase by the same proportion.
To calculate weight, we use the equation:
Weight (N) = mass (Kg) x gravitational feild strength (N/Kg)
W = m x g