Heavier things have a greater gravitational force AND heavier things have a lower acceleration. It turns out that these two effects exactly cancel to make falling objects have the same acceleration regardless of mass.
The greater an object's mass, the greater its gravitational force. The earth has a strong attracting force for objects with smaller mass (including the moon), and the sun has an attracting force on the earth and other planets in our solar system. ... The stronger the pull of gravity on an object, the greater its weight.
