The term "common sense"
ArglebargleEinsteingrrhateblargh.
Let me just say that it makes little sense to try and write down a single definition of the common meaning of weight - it can mean different things at different moments for different people. It could be e.g.the measurement on the scales, the force needed to hold a body still against the force of gravity, mass, or the force needed to hold an object still, period. The exact meaning is context-sensitive and generally people have no problem discerning between them. For example saying that "I weigh more in an ascending elevator" makes it clear that I mean the net force acting downwards; "a baloon is lighter than air" makes it clear it's about buoyancy caused by the difference in density between the baloon and the surrounding air.
In physics the general use of weight is indeed the force acting on a body in a gravitational field:
W=
am, where both
W and
a are vectors pointing from the mass m towards the gravity source.
By convention the direction towards the source of a gravitational field is denoted as a negative vector, so anybody thinking in vectors would be required to say that weight is always negative.
However, since both vectors in the equations have the same, constant direction they can be treated as scalars. In this sense there can be no negative values of vector W, as gravity is never repulsive.
If anybody were to calculate the net force acting on body suspended over(e.g.by standing on the surface of) a planetary body such as Earth, then they'd have to take into account the gravitational field at a given distance from the centre of mass of the planet, the centrifulgal force at a given latitude, the buoyancy exerted by any fluid present(possibly of varying density), coriolis force and any other inertial forces that may apply as well as tidal forces from near celestial bodies.
One could call the result "weight", but keeping in mind it would not be the definition physics uses.
Finally, there's the definition of weight used by ISO, and that is the combination of the gravitational force and the centrifugal force.
ed: grammar