Why do things fall at the same rate regardless of weight?

The answer

Galileo demonstrated and Newton later proved that gravitational acceleration is independent of mass. While a heavier object experiences a stronger gravitational pull, it also has more inertia (resistance to acceleration), and these two effects perfectly cancel out. In a vacuum, all objects fall at exactly the same rate: 9.8 m/s² on Earth. Apollo 15 astronaut David Scott famously demonstrated this on the Moon by dropping a hammer and a feather simultaneously - they hit the lunar surface at the same instant.