In a way one has to 'unlearn' heaviness/plantedness but not at the expense of losing structure and connection through the body. Move WITH someone trying to run you down or throw you and WHERE you move in relationship to THEM is even more important. You can't gain the advantage unless you understand the geometry of the whole.
Where is the 'space'? Where is the resistance? Which way is down? Where is weak? Where is the way out?
Here is a compilation clip of Mansur Isaev. He's a Judo player. Check out his footwork. That Cossack dancing really comes in handy doesn't it?
Big thanks to Steve Morris, a man with a superior understanding of movement and power and with some of the best eyes in the fight business, for finding the clip.