And the prize goes to Intruder and hans brinker for the correct answer. Congratulations to these two gentlemen!
The answer to the OP's question lies in the relationship between Vr and V2.
When considering that relationship, we must consider what, exactly, Vr actually is.
So, what is Vr? We all tend to think of it as "the airspeed at which the body is rotated for takeoff", but there is a much better answer to this question, and that is the answer given on the first line of hans brinker's post above (#18).
Intruder explained things in terms of the effect excess thrust has on the acceleration that has to occur between Vr and V2.
I'll throw in my two bob's worth by continuing along the line laid down by Intruder:
Imagine a Vr of 0 (zero) and a V2 of 150 knots. Theoretically possible, but achievable only when there is CONSIDERABLE excess thrust. If the excess thrust is not CONSIDERABLE then the starting speed (Vr) will have to be some value closer to V2. The less CONSIDERABLE, the greater the Vr (and the smaller the gap between Vr and V2).