duly (adv.)

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.

common adverbial suffix, forming from adjectives adverbs signifying "in a manner denoted by" the adjective, Middle English, from Old English -lice, from Proto-Germanic *-liko- (cognates: Old Frisian -like, Old Saxon -liko, Dutch -lijk, Old High German -licho, German -lich, Old Norse -liga, Gothic -leiko); see -ly (1). Cognate with lich, and identical with like (adj.).

Weekley notes as "curious" that Germanic uses a word essentially meaning "body" for the adverbial formation, while Romanic uses one meaning "mind" (as in French constamment from Latin constanti mente). The modern English form emerged in late Middle English, probably from influence of Old Norse -liga.