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.

early 15c., "that which is owed, what one deserves or is entitled to," from due (adj.), also compare dues. To give the devil his due "do justice to a person of supposed bad character" is from 1590s.  "Giue them their due though they were diuels" [1589]. 

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.

"delayed or withheld beyond the usual or assigned time," 1845 of unpaid bills, 1890 of unreturned library books, 1970 of menstruation, from over- + due (adj.).

"rightly, properly; adequately, sufficiently; in accordance with duty or moral obligation," late 14c., duweliche, from dewe "due" (see due) + -liche (see -ly (2)).

"resulting or due to chance; casual, unexpected," 1670s, from chance (n.).

late 15c., "in due order, duly, properly," from order + -ly (2).