Meanings
According to Michael Quinion of World Wide Words, the verb "to cotton" first appeared in the English cloth industry before the 17th century, to refer to the finishing of the newly-woven cloth. "The very first sense of the verb was to raise the nap on cloth such as wool to draw out the loose ends of the fibres before shearing it to give it a smooth finish. It may have been because freshly woven cotton has a natural fuzzy nap that means it can be sheared without first having to artificially raise it". The word "cotton" is derived from the Arabic word "qutn". Arabic traders supplied the Western world with cotton from Indus Valley, where it had grown since 5000 BCE. The word was then applied to the fine finishing of any cloth. With the boom in the cotton industry it came to represent success especially financial success. "By about 1600, 'to cotton together' 'or cotton with' a person meant you got on well together. It has plausibly been suggested it came from the use of mixtures of cotton and other fibres in clothing. A little later, cotton up meant to strike up a friendship. In the early 1800s, to cotton to somebody implied that you were drawn or attached to that person. It may be that the idea here is how well a thread of cotton sticks to the surface of cloth".
How to pronounce "cotton to":
To like; approve of, accept, or tolerate.
Example: "He tried sneaking it past them, but they didn't cotton to his attempts."