According to Aristotle, heavier bodes fell faster than lighter bodies, but Galileo realised that all matter was subject to the same laws of motion and that all bodies would fall or accelerate at the same speed provided differences in friction or wind-resistance were eliminated. Galileo also realised that the natural state of an object is rest, unless it is acted upon by an external force, and that it had an inherent resistance to move (i.e. he discovered the principle of inertia) . This realisation was to be very important for Newton.
Editors. "Galileo's laws of motion". The Literary Encyclopedia. First published 01 January 2008
[http://www.litencyc.com/php/stopics.php?rec=true&UID=453, accessed 01 April 2015.]