sweat (v.) Look up sweat at Dictionary.com
Old English swætan "perspire," also "work hard," from Proto-Germanic *swaitjan "to sweat," from the source of sweat (n.). Compare Frisian swette, Dutch zweeten, Danish svede, German schwitzen. Meaning "to be worried, vexed" is recorded from c.1400. Transitive sense is from late 14c. Related: Sweated; sweating. Sweating sickness was a sudden, often-fatal fever, accompanied by intense sweating, that struck England 1485 and returned periodically through mid-16c., described in the original citation (a chronicle from 1502) as "a grete deth and hasty."
sweat (n.) Look up sweat at Dictionary.com
Old English swat "perspiration, moisture exuded from the skin," also "labor, that which causes sweat," from Proto-Germanic *swaitaz "sweat" (cognates: Old Saxon, Old Frisian swet, Old Norse sveiti, Danish sved "sweat," Swedish svett, Middle Dutch sweet, Dutch zweet, Old High German sweiz, German Schweiß), from PIE *sweid- (2) "to sweat" (cognates: Sanskrit svedah "sweat," Avestan xvaeda- "sweat," Greek hidros "sweat, perspiration," Latin sudor, Lettish swiedri, Welsh chwys "sweat").

A widespread set of Slavic words (Polish, Russian pot "sweat") is from Old Church Slavonic potu, related to peku "heat," cognate with Latin coquere.

The Old English noun became Middle English swote, but later altered to the current form under the influence of the verb. Sweat of (one's) brow as a symbol of toil is from Gen. iii:19. Sweat equity is from 1968. Colloquial no sweat "no problem" attested from 1963.