Earlier quoted context omitted.
It is amusing how many of my peers still hold to the notion that heavier things fall faster. Not a higher terminal velocity, but the intuition that they accelerate faster. Hilariously tough for folks to shake.
There is a larger gravitational force on heavier things because they're heavier. Trouble is, they also have more inertia, which exactly counteracts the larger force (because of the principle of equivalence) and so they fall at the same acceleration as lighter objects.
You can say that two larger things attract each other more than smaller things. Especially as they get closer to each other. Catch, of course, is all things on the earth are in the noise range compared to, you know, the earth. If you are talking about gravity and acceleration on the earth, you are talking about 9.8 m/s^2. Pretty much period.
And yes, there are terminal velocities that impact maximum speed. Acceleration, though, is not velocity.