This is question is coming from what Ive read in my college history book, so bear with me. Perhaps I do not understand what exactly inertia and gravity are, but as far as I know, inertia is the idea that an object in motion continues forever until an external force acts on this. An external force that often stops or changes the motion of an object is gravity, and at the time Galileo discovered the principle of inertia,
The short answer is that Newton didn't discover gravity. Everyone knew about gravity (it would be hard not to), they just didn't understand how it worked. Galileo, like most people, understood that some force was pulling things down, and unlike most people, this helped inform his understanding and formal statement of inertia. Newton built on Galileo's knowledge. (Rarely does someone discover something completely new. Most scientific discoveries are built on a preexisting body of knowledge that has known gaps. Newton's formal work on gravity filled one such gap.)
For more details, check here: http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/DiscoveringGravity.htm
Edit: a bit unrelated, but Apollo 15 astronauts testing Galileo's work on gravity. Hopefully this is clear and accessible example of how knowledge is amassed years before it is "discovered." http://www.youtube.com/watch?v=KDp1tiUsZw8
You might do better in r/askscience. Inertia is not only related to gravity, but to any force.