This comes back to the concept that if you drop objects of different masses in a gravitational field they will all fall at the same rate.
It might not seem intuitive that is how it works, because as you point out something with a greater mass will have a greater attraction under the force of gravity. That is why more massive things are heavier, right? But more massive things also have greater inertia or resistance to acceleration.
It turns out that the increased inertia exactly cancels out the increased attraction of gravity, so a feather and a dumbbell fall at the same speed in a vacuum.
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