What we conveniently forget is what I just parenthesized as “Ethereal Relativism”. Before Einstein’s work, the ether was taken to be something that gives motion a sense of absoluteness. Ether was the absolute measure or reference of motion, therefore all motion seemed to be known as absolute. But its widely silent that Galileo and Newton worked in a frame-work of Physics or laws of nature where a frame of reference keeps motion relative, and not absolute: a concept known as Galilean Relativity.
In other words, if there is an object falling under gravity, in telling our story, we almost forgot that, there can also be a situation where, the relative motion of the falling object, can be studied; with or without the gravity acting on the object. In other words, still, the central question is to ask; did this single object fall faster or slower w.r.t. a situation when there is no gravity? Was it known or not, to Galileo, that, this object can be tested; to be falling faster in presence of the gravity causing object.
As we know today: Gravity causes objects to fall faster, it does not cause them to fall in the first place, between heavier and lighter objects it does not make any one of them to fall faster than the other and this is a force of central attraction to the proportion of; strength being as higher as the square of separation is, less.