late 14c., (late late 13c. in surnames and place names), cobelere "one who mends shoes," of uncertain origin. It and cobble (v.) "evidently go together etymologically" [OED], but the historical record presents some difficulties. "The cobbler should stick to his last" (ne sutor ultra crepidam) is from the anecdote of Greek painter Apelles.
On one occasion a cobbler noticed a fault in the painting of a shoe, and remarking upon it to a person standing by, passed on. As soon as the man was out of sight Apelles came from his hiding-place, examined the painting, found that the cobbler's criticism was just, and at once corrected the error. ... The cobbler came by again and soon discovered that the fault he had pointed out had been remedied; and, emboldened by the success of his criticism, began to express his opinion pretty freely about the painting of the leg! This was too much for the patience of the artist, who rushed from his hiding place and told the cobbler to stick to his shoes. [William Edward Winks, "Lives of Illustrious Shoemakers," London, 1883]
[The tale is variously told, and the quote is variously reported: Pliny ("Natural History" XXXV.x.36) has ne supra crepidam judicaret, while Valerius Maximus (VIII.xiii.3) gives supra plantam ascendere vetuit. The version cited here confessedly is for the sake of the book name]