The size of a thing relative to a reference, and the act of changing it. Also a graded series for measuring.
Latin scala (a ladder, a flight of steps), from scandere (to climb); a scale is graduated like a ladder's rungs, each step measured against the ones before and after it.
The size of a thing measured against a reference, or a graded series for measuring at all — both keep the ladder's own idea of climbing by even, comparable steps.