You are forgetting the $m$ in Newton's 2nd law:

$$\sum F=ma$$

Yes, some bodies feel a stronger gravitational force, so $\sum F$ is larger. But then they also have a larger mass $m$. Doubling one will double the other. So $a$ doesn't change.

The acceleration $a$ turns out to alway be equal to $a=-9. 82\mathrm{\frac m{s^2}} $. The numerical value is usually given the symbol $g$.

You are forgetting the $m$ in Newton's 2nd law:

$$\sum F=ma$$

Yes, some bodies feel a stronger gravitational force, so $\sum F$ is larger. But then they also have a larger mass $m$. Doubling one will double the other. So $a$ doesn't change.

The acceleration $a$ turns out to alway be equal to $a=-9. 82\mathrm{\frac m{s^2}} $. This numerical value is usually given the symbol $g$.