Also, you don't 'fly' at Vr. You start to rotate. Liftoff occurs at some, higher, speed - depending on the speed and rate you rotate at, the acceleration the aircraft has, and the speed you need to lift off at a given AoA. So you can't necessarily assume that Vr follows the speed-squared relationship.
Consider - even if you didn't rotate, eventually you'd be fast enough (assuming a long enough runway) to lift off at nominally zero AoA. You couldn't correlate that speed with a normal technique at a different weight.