Velocity of a Catalyzed Reaction

In considering the progress and velocity of a catalyzed reaction, we have some additional things to think about. In the uncatalyzed reaction, we have seen how the substrate concentration affects the velocity
In a catalyzed reaction, the concentration of the enzyme [E] also affects the velocity:

In a reaction with a very high substrate concentration, the enzyme will be saturated
In this situation, doubling the amount of enzyme will double the initial velocity of the reaction
Conversely, if substrate concentration is very low, doubling the enzyme concentration will not double the velocity
Why not?