Why Does the Army Call NCOs "Sergeant" and Officers "Sir"?

Throughout my Army career, I have been taught that we refer to NCOs as "Sergeant" (or, beginning with Master Sergeant, their full rank) but we refer to Officers as "Sir" or "Ma'am." However, recently I was challened by an E-9 in the Air Force (Chief Master Sergeant, I think) to find out more about this. Is this simply the unwritten rule, a part of Army customs and courtesies? And, if it is, where did this come from? Or is this actually written somewhere, in a regulation I have not found yet?

Note that at no point am I saying this is incorrect. I am just trying to get some actual facts on the tradition, so that, as an NCO, I know more about the facts behind the traditions/customs/courtesies.