The constant acceleration of all objects can be deduced logically.

Consider a stone that falls with a given acceleration. If heavier objects fell faster than lighter objects, a stone with twice the weight would have to fall with a greater acceleration. We could construct a double-weight stone by tying two stones together side-by-side and dropping them at once, but it would be equivalent to simply dropping them side by side. Equally, if the configuration were dropped horizontally, with one stone leading the other, this would only fall faster than a single stone if the leading stone accelerated faster than the trailing stone, but that would contradict the assumption that the two stones are both the same weight.

Consider a stone that falls with a given acceleration. If heavier objects fell faster than lighter objects, a stone with twice the weight would have to fall with a greater acceleration. We could construct a double-weight stone by tying two stones together side-by-side and dropping them at once, but it would be equivalent to simply dropping them side by side. Equally, if the configuration were dropped horizontally, with one stone leading the other, this would only fall faster than a single stone if the leading stone accelerated faster than the trailing stone, but that would contradict the assumption that the two stones are both the same weight.