1757, "situated between two things;" 1818 as "serving as a mediator;" from French intermédiaire (17c.), from Latin intermedius "that which is between" (see intermediate). As a noun, "one who acts between others" from 1791 (Medieval Latin intermedium also was used as a noun). An earlier adjective was intermedial (1590s).

Intermediary, n., is, even with concrete sense of go-between or middleman or mediator, a word that should be viewed with suspicion & resorted to only when it is clear that every more ordinary word comes short of the need. [Fowler]

also middle-weight, "boxer or jockey of intermediate weight" (between a lightweight and a heavyweight), 1842, from middle (adj.) + weight (n.).

"medium in rank, condition, or degree; intermediate," 1540s, from Middle English medlinge "intermediate between two things" (late 14c.), from middle (adj.) + present-participle suffix -ing (2). Used in trade to designate the second of three grades of goods. Hence "only medium, neither good nor bad" (1650s). As an adverb, "tolerably, passably," by 1719.

also nonstop, "that does not stop," 1903, from non- + stop (n.); originally of railway trains not making intermediate stops. As an adverb by 1920.