Consider this scenario – a customer wants a new report or new screen added to their requirements, after they have been signed off. Quoting for that is relatively easy, however, what happens if the change impacts many areas of the development? There might be only 1 change but all impacted areas need to be retested.
Having a size measure (e.g. function points) can quantify how many areas are affected and, depending on the current life-cycle phase of the project, a % applied to determine the overall impact of the change. Multiplying that size by the $/function point determines the quote price. This is a transparent method of adjusting a quote for size that is quantifiable by both customer and developers.