Thus, we must be careful that we are not using the same thing to measure the black hole as we are using to represent the speed. The sigma is measured far away from the black hole where it doesn't have any influence. We are too far away from it and it has too small a mass. Thus, how does such a small thing in the middle of the galaxy end up correlating so well with the rest of the galaxy. The belief is that they are related during their formation process.
Sigma is a measure of how much the galaxy contracted.
Thus, it appears that black holes and bulges form at the SAME time. To be more correct I should say that most of the mass growth for the black hole and for the galaxy was governed by the same process. For example, as we pile more and more mass on the black hole, the energetics increase and we end up with stronger jets and winds. These push the infalling material out and we stop the growth of both galaxy and black hole. However, it is still a huge puzzle as to how such a small component can have such a significant effect.