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Gravitational force on an object is $F_g = mg$, so it is proportional to mass $m$. Newton's second law states $F=ma$, rearranged as $a=\frac{F}{m}$. For gravitational acceleration, when $F=F_g$, $g=\frac{F_g}{m}$; if $F_g$ is proportional to $m$, $g$ (acceleration due to gravity) ends up independent of mass, but in the context of the relationship between force, mass, and acceleration, acceleration is the quantity inversely proportional to mass when force is fixed (or here, for gravitational systems, the resulting acceleration from the gravitational force follows the inverse mass relationship from Newton's second law).
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acceleration (or acceleration due to gravity)