early 14c., "customary, regular;" mid-14c., "owing, payable," from Old French deu, past participle of devoir "to owe," from Latin debere "to owe" (see debt).
In reference to points of the compass (e.g. due east) it is attested from c.1600, originally nautical, from notion of "fitting, rightful." As an adverb from 1590s; as a noun from early 15c. Prepositional phrase due to (much maligned by grammarians) is from 1897.
To serve and suffer such that one deserves what good comes to one; Go Through the Mill: We elderly have paid our dues
[1943+; an isolated example is found in 1878]