Firstly, 9.81 feet per second is a speed not an acceleration. Acceleration due to gravity is 9.81 metres per second per second. I just dropped out of a University module on relativity. What we experience as gravity is a consequence of how mass-energy curves spacetime. Objects tend to move along paths of least effort, essentially looking for the shortest path through curved space.

More massive objects curve spacetime more than less massive objects, just as a massive ball on a rubber mat curves the rubber mat more than a lightweight ball.