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"low in price, that may be bought at small cost," c.1500, ultimately from Old English noun ceap "traffic, a purchase," from ceapian (v.) "trade," probably from an early Germanic borrowing from Latin caupo "petty tradesman, huckster" (see chapman).
The sense evolution is from the noun meaning "a barter, a purchase" to "a purchase as rated by the buyer," hence adjectival meaning "inexpensive," the main modern sense, via Middle English phrases such as god chep "favorable bargain" (12c., a translation of French a bon marché).
Sense of "lightly esteemed, common" is from 1590s (cf. similar evolution of Latin vilis). The meaning "low in price" was represented in Old English by undeor, literally "un-dear" (but deop ceap, literally "deep cheap," meant "high price").
The word also was used in Old English for "market" (cf. ceapdæg "market day"), a sense surviving in place names Cheapside, East Cheap, etc. Related: Cheaply. Expression on the cheap is first attested 1888. Cheap shot originally was U.S. football jargon for a head-on tackle; extended sense "unfair hit" in politics, etc. is by 1970. German billig "cheap" is from Middle Low German billik, originally "fair, just," with a sense evolution via billiger preis "fair price," etc.