Weight

Weight is a force and is measured in newtons:

$W = mg$

where $m$ is the mass (kg) and $g$ is the gravitational field strength (N/kg).

Weight changes with location because $g$ varies. An object weighs less on the Moon ($g = 1.6$ N/kg) than on Earth ($g = 9.8$ N/kg), but its mass stays the same.

Weight always acts vertically downward toward the centre of the Earth (or whatever body is creating the gravitational field). It is measured using a newton meter.