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According to the FAA's definitions in 14 CFR 1.1, a Large aircraft is an "aircraft of more than 12,500 pounds, maximum certificated takeoff weight." I have heard this threshold was set based on the DC-3, but that makes no sense to me. Also, there doesn't seem to be any common-sense/international connection to kilograms (i.e. 12,500 pounds is roughly 5670 kg, not a nicely rounded-off 5700 kg).
What is the origin of 12,500 pounds being the cutoff between Large and Small aircraft?
The answer by pithblot is more or less correct. The 12,500 lb. limit was chosen as an approximate halving of the DC-3 gross takeoff weight. Consider the following quote:
As noted earlier, when first promulgated, the 12,500 lb. weight limit could be understood in light of the general use of the DC-3, an aircraft with a maximum gross takeoff weight of 25,000 lbs. and carrying from 21 to 25 passengers in airline service... The imposition of a 12,500 lb. gross weight maximum, by effectively limiting the number of passengers that could be carried as well, did indeed protect the local service carriers' interests.
(U.S. House of Representatives, 94th Congress, 2nd Session, 1976, pg. 48)
References: U.S. House of Representatives, 94th Congress, 2nd Session. (1976). The future of aviation: Hearings before the subcommittee of aviation and transportation R. & D. of the committee on science and technology [no. 82]. Washington, D.C.: U.S. Government Printing Office. Retrieved from Google Books.
The DC3 was the backbone of reliable air transportation and way ahead of its time....the wonder metal Aluminium. Deice. Autopilot. Two pilots flight crew. Hostess. Blind flying equipment. Comfortable. Reliable.
It set the standard in many areas...I read somewhere that the rudder force limit OEI of 180 lbs is derived from the DC3. Likewise, the Gulfstream 1 cabin crossection was chosen to be same as the DC3, (I guess because it worked - it was comfortable and looked right) and this carried through to the G2 and many corporate jets.
A light aircraft was considered to be less than half the weight of a DC3 - I was told this many years ago. Can't give a reference, can't confirm if it's true or not. It's just one of those aviation things, maybe even common sense?
If you take a look at FAA FAR 14 CFR 23.3 - Airplane categories. you can see the amendment history linked at the bottom. This will take you through a series of changes made to the regulation as well as to the creation of part 23 in 1964 and some provide some background/history for some of the changes. It looks like in 1964 the 12,500 LB limit was not part of Part 23. It was likely included elsewhere so I cant yet trace this full history. However in the amendments that appeared as part of Federal Register: 52 Fed. Reg. 1619 (Jan. 15, 1987). (Page 1806) they go into some specifics and it appears that the weight was chosen as it was somewhere in the middle of the over all range.
Since 1953 the airworthiness standards have distinguished small from large airplanes by a 12,500 pound maximum certificated takeoff weight -(MCTW) limitation regardless of the type of operation. When this weight limitation was established, little concern was expressed that this demarcation would eventually become questionable with regard to airworthiness standards for an airplane of the commuter category. At that time, there were few airplane designs near this 12,500 pound limitation; i.e., they were either considerably above or below that weight.
Effectively at the time (1953) all "small" planes were well below that and all "big" planes well above that. Unfortunately this does not shed any light on your DC-3 note.
