Hi again elle
In an expression like (to take a simple one)
F=ma
the m can take any value, thus affecting the acceleration as a result of the force applied
For a given body, the same "m" appears in the equation giving the gravitational force, so it cancels out, and all bodies fall at the same acceleration (ignoring air resistance)
You are right, though, that changing the gravitational force will change the weight of a body, but not its mass.
Sorry if that takes you too far back to A level Physics!