Where does the term 'double-jointed' come from?

Sadly, the OED (through the 1987 Supplement) does not provide an etymology. My guess is that it is a metaphorical extension from joinery or mechanics. There are many sorts of double hinges (often called 'double-action hinges'); or it would be very natural to refer to what we now call a universal joint or U-joint as a 'double joint'. All of these are designed to provide a rotatory joint with more freedom of movement than normal: either more degrees of rotation about a single axis, or rotation about more than one axis, or both.

As I understand 'double-jointed' refers to the idea that such people have opposing joints, which allow them to "fold" their knees/elbows etc. in both directions with equal ease.

Naturally this isn't accurate as we know people considered to be double-jointed simply possess extremely flexible joints (or rather - ligaments) which allow them to stretch their appendages farther than most people.

The OED’s definition is ‘Having joints that permit a much greater degree of movement of parts of the body than is normal’. The earliest supporting citation is from 1831. A citation from 1961 tells us that ‘Anatomists can only plead ignorance of the minor structural differences that must distinguish the normal joint from the double jointed variety.’

As someone who played with a ton of Lego, a double joint would account for flexibility in that way, but is obviously not a physiological answer in most cases.

My guess is that either the term originates from a mechanical analog, or a funky mutation in which someone actually has more joints. That's entirely speculative, but I've seen much, much stranger mutations.