To give an example of what I'm trying to understand:

To accelerate to a given speed or maintain that speed with a tyre pressure of e.g. 100PSI requires a certain amount of energy. If that amount of energy is held constant, and the tyre pressure is dropped to e.g. 80PSI, how much lighter would my bike need to be to attain / maintain that speed.

What prompts my question is the observation that many cyclists who commute have under-inflated tires, yet have paid a premium for aluminium over steel.