I'm on my phone atm, in a boring conference room. So I'll keep it short, and whoever wants to know more can ask me whatever.

But yeah, certainly; there was lively discussion about the power which moved bodies downward. The word gravity was used already for this, though it meant something more like mass, density, weight, heaviness, etc. The clear distinctions between all those concepts were gradually being worked out by natural philosophers in the late medieval and early modern period.

For a long time, the dominant account of this downward attraction was what we call the Aristotelian account. According to Aristotle, all bodies had a natural place within the universe, with heaviest things striving towards the center of the cosmos and the lighter elements striving for a place more outward. So earth would strive to the center because that is its natural place. Likewise, water would also tend to move downwards, striving to its own natural place. Air and fire are the lighter elements, and would strive upwards. This way you get a natural layer model of earth-water-air-fire. Fire, being the lightest of the earthly elements, strived to the highest place within the sublunar realm. Beyond the moon, there was generally considered to be a fifth element which was more perfect than any of the earthly elements, and more subtle. So beyond the moon a very there ruled a very different physics, of perfect bodies with perfect motions, while below the moon everything was corruptible and chaotic.

This conception gradually changed in the aftermath of the 1277 condemnations in Paris, and the subsequent discussions of other worlds and multiple universes, which caused people to reconsider the structure of the universe.

Our attractive model of a gravitational force or field only developed after 1600, though even here it remained highly problematic what the force is and which body is doing the work. Gilbert's De Magnete was certainly a big influence in these debates, as was Descartes' vortex model and Kepler's cosmology. From these sources, Newton constructed his own theory, which became so influential not because it gave a satisfactory explanation of gravity (it didn't), but because it refocused the effort towards producing a functional mathematical model of gravitational attraction.

The typical way we (non-physicists) nowadays think about gravity is more or less a child of later 18th accounts of how gravity works, when ether and field theories came to the foreground. Prior to that many explanations of Newtonian gravity had a strong theological foundation in which the force of gravity was considered a direct act of God.

If I explained things poorly or you have any questions, please ask. I love talking about this subject!🙂