When the force of gravity is doubled, for example, we have 2W = 2mg = m (2g) and thus we have 2-g's. If the force is tripled, we'd have 3-g's, etc.
Of course we can't really turn up the value of g, that comes from GM/r^2 alone. But we can add artificial gravity by invoking centrifugal force and its radial acceleration Ar = V^2/r. So if we spin something fast enough, we can get Ar = g. And that can be added to the natural g to give g + Ar = g + g = 2g. Or we can spin that something even faster so that g + Ar = g + 2g = 3g, and so on.
In which case, the forces would be W, 2W, and 3W with the centrifugal forces adding to the natural weight of something. So we can say we have 1-g, 2-g, and 3-g forces respectively. But not the G, which remains the same throughout.