Superman is at rest in space when he throws an asteroid that has more mass than he does. Which moves more faster, Superman, the asteroid, or both at the same speed.

Since the asteroid has more mass than Superman, it has more inertia. Superman will move away from the asteroid at a greater rate than the asteroid moves away from him. The more of his super strength he uses to toss the asteroid simply increases his rate of speed away from it.

That's stupid... Everyone knows that Superman wouldn't move unless he wanted to move. ::)

Unless there is another body nearby lending to the situation it's own gravitational influence.

The greater the mass the greater the gravitational influence?