sweepstakes n.

early 14c., "make clean by sweeping with a broom;" mid-14c., "perform the act of sweeping," of uncertain origin, perhaps from a past tense form of Middle English swope "sweep," from Old English swapan "to sweep" (transitive & intransitive); see swoop (v.), or perhaps from a Scandinavian source. Related: Swept; sweeping.

From late 14c. as "hasten, rush, move swiftly and strongly;" also "collect by sweeping." From c. 1400 in transitive sense "drive quickly, impel, move or carry forward by force;" mid-15c. as "clear (something) away." Meaning "win all the events" is 1960, American English. Sense of "pass systematically over in search of something" is from 1966. To sweep (someone) off (his or her) feet "affect with infatuation" is from 1913.

"that which is placed at hazard as a wager, the sum of money or other valuable consideration which is deposited as a pledge or wager to be lost or won according to the issue of a contest or contingency," 1530s, perhaps from stake (v.2), which is attested a few years earlier, but both the noun and verb are of uncertain origin. Perhaps literally "that which is fixed or put up," either from a particular use of stake (n.1) "stake, pole," or from the notion of "a post on which a gambling wager was placed" (but OED points out there is "no evidence of the existence of such a custom"). Weekley suggests "there is a tinge of the burning or baiting metaphor" in this usage.

Meaning "the prize in a contest of strength, skill, speed, etc." is by 1620s; plural stakes, "sum of money to be won in a (horse) race," is recorded by 1690s (compare sweepstakes). Meaning "an interest, something to gain or lose" is by 1580s; hence have a stake in "have an interest in the turn of events, have something to gain or lose" (1784). The phrase at stake "state of being laid or pledged as a wager; state of being at hazard or in peril" is from c. 1600.

mid-13c., "stroke, force," from sweep (v.). Meaning "act of sweeping" is from 1550s. From 1670s as "range, extent of a continued motion." In reference to police or military actions, it is attested from 1837. Sense of "a winning of all the tricks in a card game" is from 1814 (see sweepstakes); extended to other sports by 1960. Meaning "rapid survey or inspection" is from 1966. As a shortened form of chimney-sweeper, first attested 1796.