Gravitational field strength: the force on each kilogram

1. "Per unit mass" means per kilogram, and that phrase is what earns the mark; "the pull of gravity" scores nothing.
2. There is no formula sheet, so recall the equation and be ready to rearrange it into $W=mg$ and $m=W/g$.
3. Near the Earth's surface $g\approx 9.8N/kg$, though some questions tell you to use $10N/kg$; always use the value given.
4. On the Moon $g\approx 1.6N/kg$, about six times weaker, which is why the same object weighs about six times less there.

Why g is also the acceleration of free fall

1. Gravitational field strength is equivalent to the acceleration of free fall: these are the same number written in different units, not two quantities that happen to match.
2. Since $1N=1kg\times 1{m/s}^2$, dividing a force in newtons by a mass in kilograms leaves ${m/s}^2$, so $N/kg$ and ${m/s}^2$ are the same unit written two ways.
3. An object in free fall has only its weight acting, $W=mg$, so $mg=ma$ and therefore $a=g$; the mass cancels, which is why all objects fall at the same rate when there is no air resistance.

Weight as the effect of a gravitational field

1. Weight is not something an object carries by itself: it is the effect of a gravitational field on a mass.
2. Every mass creates a field around it; a second mass placed in that field feels a force, and that force is its weight.
3. The field decides the weight: move a fixed mass into a stronger field and its weight rises, into a weaker one and its weight falls; the mass never changes.
4. The field belongs to the place, not the object: $g$ states how many newtons each kilogram would feel there, whether or not anything is present.
5. Near the Earth's surface the field is uniform, directed vertically downwards, so weight acts straight down and $g$ is effectively constant over the heights met here; far away the field is radial and weakens with distance.