The acceleration of a falling object acted on by gravity only is g.
Because the force of gravity on the object is the only force acting on it, its weight (in newtons), W = mg, where m = the mass of the object (in kg).
When an object is in equilibrium, the suport forceo on it is equal and opposite to its weight.
Therefore, an object placed on a weighing balance exerts a force on the balance equal to the weight of the object.
Thus the balance measures the weight of the object.
g is also referred to as the gravitational field strength at a given position, as it is the force of gravity per unit mass on a small object at that position.
So the gravitational field strength at the Earth's surface is 9.81N/kg.
Note that the weight of a fixed mass depends on its location. For example, the weight of a 1kg object is 9.81N on the Earth's surface and 1.62N on the Moon's surface.
The mass of an object is a measure of its inertia, which is ist resistance to a change in motion.
More force is needed to give an object a certain acceleration than to give an object with less mass the same acceleration.
The scale on a top pan balance is usually calibrated for convenience in grams or kilograms.