Well, the term, "Aye, means "Yes" And certainly in the old days, respect and ceremony were much more important and 'due' than they are today. So, it would have sprung from a blend of both.

It's a naval term, the response to an order given by the captain of a ship. "Aye" means yes, or I will comply. "Aye, aye" simply emphasises it. Captain is from Old French capitaine, and from the Latin capitaneus, meaning chief. "Aye, aye, skipper" is a more familiar form.

1) "“Aye, aye, Sir” is the proper response for a sailor to give to a superior. As Charles from Atwood confirmed in his call-in, the double aye is meant to convey that the order has been both received and understood. There is some confusion over the origin of the term, however, probably because there are two ayes. One of them meant forever or always. The other meant yes. There is some speculation that the latter came from the former, the transition being something like always/by all means/with certainty/yes. [Oxford English Dictionary] But militating against this is the fact that the first written instances spell that version of yes as I: • “If you say I, syr, we will not say no.” [1576, Tyde Taryeth no Man] • “Nothing but No and I, and I and No.” [1594, Drayton, Idea, 57] At various times it was also spelled ey, ai, ay, and hye. So the suggestion found on some web sites that aye is an initialism for “at your [service] ever” lacks any foundation. Aside from its nautical use, it is the formal word used to signal a yes vote in the British House of Commons. And, to get completely off the track, aye-aye (as listener Susan of Copemish shared with me) is the name of a nocturnal tree-dwelling primate found only in Madagascar. The best guess for the animal’s name is that it came from some now defunct language native to Madagascar and may have been onomatopoeic in origin." Source and further information: http://verbmall.blogspot.com/2007/10/aye-aye-sir.html 2) "‘aye aye, sir’, the correct and seamanlike reply on board ship on receipt of an order. In the days when officers were rowed ashore, or to their ships, ‘Aye aye’ was also a boat's reply in the Royal Navy when hailed from a ship if it had a commissioned officer below the rank of captain on board. If no commissioned officer was on board, the reply was ‘No No’; if a captain was on board the reply was the name of his ship, and if an admiral, the reply was ‘flag’. Boats were hailed in this fashion so that those on watch would know the form of salute required when officers arrived on board." Source and further information: http://www.encyclopedia.com/doc/1O225-ayeayesir.html "In the Marine Corps, the nautical expression "Aye, Aye, Sir" is used when acknowledging a verbal order. "Yes, Sir" and "No, Sir" are used in answer to direct questions. "Aye, Aye, Sir" is not used in answer to questions as this expression is reserved solely for acknowledgement of orders." Source and further information: http://usmilitary.about.com/od/marines/a/customs.htm "Aye Aye, Sir (nautical) The correct and seamanlike reply, onboard a U.S. Navy (or Royal Navy) ship, on receipt of an order from an officer. It means "I hear the command, I understand it and will comply with the order."" Source and further information: http://en.wiktionary.org/wiki/Aye_Aye,_Sir