Is gravity acceleration (g) per unit mass (kg)?. It must be. Gravity = mass (m) x g. This then means that gravity is purely acceleration and all objects fall at the same rate in vacuum regardless of their weights. Gravity = m x g, i.e. Kg x g /Kg = g.

 

I'm guessing you are studying high school physics or applied maths, and what you are referring to is the vertical acceleration due to gravity felt by all material bodies on Earth.
This is normally given the symbol g and has an (average) metric value of 9.81 metres per second per second, you you are correct this is an acceleration.

 

On 3/26/2021 at 3:59 PM, Phys1 said:

Is gravity acceleration (g) per unit mass (kg)?. It must be. Gravity = mass (m) x g. This then means that gravity is purely acceleration and all objects fall at the same rate in vacuum regardless of their weights. Gravity = m x g, i.e. Kg x g /Kg = g.

No, that is the acceleration due too gravity.  It is not gravity itself.  Gravity, since this is posted under "Classic Physics" is a force that acts between any two bodies with mass and  is given by [tex]\frac{-GmM}{r^2}[/tex] were "G" is a universal Constant, "m" and "M" are the masses of the two objects and "r" is the distance between them (more precisely, between their centers of mass).