"put or take off" an article of clothing, especially a hat or cap, late 14c., doffen, a contraction of do off, preserving the original sense of do as "put." At the time of Johnson's Dictionary  the word was "obsolete, and rarely used except by rustics," and also in literature as a conscious archaism, but it was saved from extinction (along with don (v.)) by Sir Walter Scott. However, dout and dup did not survive. Related: Doffed; doffing.
updated on September 26, 2018