Weight
One of Newton's crucial realizations
(supposedly stimulated by the impact of an apple on his head)
was that objects "fall" (accelerate toward the center of the Earth)
because they are acted upon by the force of the Earth's gravity,
FG, which is proportional to the object's mass m
as well as the Earth's mass ME
and the inverse square of the distance R from the center of the Earth.
Since both ME and R are essentially the same
everywhere near the surface of the Earth, and the acceleration g
caused by FG is inversely proportional to the object's mass m,
all objects fall (near the surface of the Earth)
with the same acceleration g = 9.81 m s-2
unless acted upon by additional forces, such as air friction
or the upward "normal force" of the ground when the object rests on it.
Conversely, the magnitude of the force of gravity on an object of mass m
is FG = m g. This is called its weight
(on the Earth's surface).
Weight, unlike mass, is not an intrinsic property of an object.
The weight of the same object would be different on Mars, for example.
Note that the weight is measured in N whereas the kg is a unit of mass, not force.