c. 1300, derken, "to make dark or darker, deprive of light;" early 14c. (intransitive), "to grow or become dark," from dark (adj.) + -en (1). The more usual verb in Middle English in both senses was simply dark, as it is in Chaucer and Shakespeare, and darken did not predominate until 17c. The Anglo-Saxons also had a verb sweorcan meaning "to grow dark."
Meanings "grow less white or clear, turn a darker color" and "render less white or clear" are from late 14c. Figurative sense of "render gloomy, sadden" is from 1742. To darken(one's) door (usually with a negative) "enter one's house as a visitor," usually with an implication of unwelcomeness, is attested from 1729.