mid-14c., "customary, regular, right, proper;" late 14c., "owed, payable as an obligation, owing by right of circumstance or condition," from Old French deu, past participle of devoir "to owe," from Latin debere "to owe," originally, "keep something away from someone," from de- "away" (see de-) + habere "to have" (from PIE root *ghabh- "to give or receive").
Of actions, "conscientious, careful," late 14c. Meaning "that is to be expected or looked for" is by 1833. Phrase in due time "at a set time; at an appropriate time" is from late 14c. Due to is from early 15c. as "deserved by, merited by;" also "owing to." It is attested from 1660s as "attributable to as a cause or origin." Its use as a prepositional phrase (much maligned by grammarians) is by 1897.
1590s, "duly," from due (adj.). In reference to points of the compass, "directly, exactly" (as in due east) it is attested from c. 1600, originally nautical, from notion of "fitting, rightful."
"fee for membership," 1660s, plural of due (n.) in the sense "payment legally due or obligatory" (1540s). To pay (one's) dues in the figurative sense "undergo hardships to gain experience" is from 1943.