due (adj.) Look up due at Dictionary.com
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 (as in 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.