My wife asked me about the colloquial phrase cotton to ‘take a liking to,’ and (as often happens) I had no idea where it came from, so I did some research and discovered nobody else really does either. The OED, in an ancient entry (first published 1893), gives the primary sense of the verb as “To form a down or nap on; to furnish with a nap, to frieze,” adding that it’s obsolete, and various other senses (“To furnish or clothe with cotton”) before getting to branch II, the figurative senses, “To prosper, succeed, ‘get on’ well. Obs.,” ” To ‘get on’ together or with each other; to suit each other; to work harmoniously, harmonize, agree,” “To agree, to fraternize,” and “To ‘take’ to, attach oneself to; to become drawn or attached to,” of which it says “The original notion in branch II is uncertain.”
So I turned to The Phrase Finder, which has an entry Cotton on to that gives a full discussion, beginning with the information that the phrase cotton on to in the sense “To get to know or understand something” “appears to be limited in usage to the UK and other countries that were previously part of the British Empire, notably Australia and New Zealand. In the USA, especially in the southern states, ‘cotton to’ is used, with the slightly modified meaning of ‘take a liking to’.” It then goes into theories of origin:
As early as 1648, in a pamphlet titled Mercurius Elencticus, mocking the English parliament, the royalist soldier and poet Sir George Wharton used ‘cotton’, or as it was spelled then ‘cotten’, as a verb meaning ‘to make friendly advances’. ‘Cotten up to’ and ‘cotten to’ were both used to mean ‘become friendly with’. Whether this was as a reference to the rather annoying predisposition of moist raw cotton to stick to things or whether it alluded to moving of cotton garments closer together during a romantic advance isn’t clear. [...] ‘Cottoning on’ as we now use it derives from the meaning of ‘attaching oneself to something’, specifically an attachment to an idea that we haven’t encountered before. It would seem to be a reasonable bet that at least one of the variants of this phrase would have been coined in one of the major English-speaking cotton producing regions of the world, for example India or the USA. Not so; which gives more credibility to the notion that this phrase has little to do with the cotton plant.
So it remains a mystery, but at least we know a little more than we did before.