There isn't a place on the face of the Earth where there is no gravity acting. This means that every object we ever come across is located in the Earth's gravitational field and is therefore acted upon by at least one force, the force due to gravity.
To keep the physical basis of the interaction in mind we suggest you call this the gravity force on the object (purists might prefer the gravitational force – but that's just much harder to spell). Gravity acts towards the centre of the Earth or, more simply, downwards. The force arrow representing the gravity force is best drawn from the centre of an object in a direction straight downwards.
The gravity story, of course, goes way beyond the Earth. Gravity is a universal force which acts between any two masses wherever they might happen to be in the universe. It's also what holds stars and planets together: that it pulls from the centre of one mass to the centre of another provides the explanations for why these objects are nearly perfectly spherical. (There is more on gravitational force in the Gravity and Space episode in the SPT: Earth in space topic.)
It is within our everyday experience that some things weigh more than others. Just try lifting them. Weighing machines measure how much force you need to hold an object up steadily. So it seems simple to call this supporting force the
For example, in supermarkets you'll find top pan scales and also hanging basket scales. Both instruments use the pull of gravity to measure the weight of groceries. They work on the principle of finding the upward force required to stop the groceries from falling to the ground. When a measurement is taken, the upward force from the weighing machine, or scales, balances the downward pull of gravity. This is an example of two forces in equilibrium. Weight then is an everyday name for this supporting force, which is measured in newtons. Weighing machines show the magnitude of this force.