early 14c., equite, "quality of being equal or fair, impartiality;" late 14c., "that which is equally right or just to all concerned," from Old French equite (13c.), from Latin aequitatem (nominative aequitas) "the uniform relation of one thing to others, equality, conformity, symmetry;" also "just or equitable conduct toward others," from aequus "even, just, equal" (see equal (adj.)).
In law, "fairness in the adjustment of conflicting interests; the settlement of controversies by the dictates of good conscience" (natural equity), late 14c., from Roman naturalis aequitas, the general principles of justice which corrected or supplemented the legal codes ("governed by benevolence, while justitia yields to another only what is strictly due," Lewis & Short).
Hence, in England and U.S., also "justice based on such principles, the system of jurisprudence as to what is fair and what is not," and "a court or jurisdiction in which these doctrines are applied" (1590s).
The Latin word also meant "a quiet, tranquil state of mind; moderation, evenness of temper."
The L. æquitas was somewhat influenced in meaning by being adopted as the ordinary rendering of Gr. ἐπιεικεια ...,which meant reasonableness and moderation in the exercise of one's rights, and the disposition to avoid insisting on them too rigorously. [OED]
From 1620s as "an equitable right, that to which one is justly entitled," especially a right recognized by courts of equity that is not provided for in the common or statute law (such as certain property rights of wives). Equities, "the ordinary shares of a limited company," carrying certain rights to assets and profits, is attested by 1904.
By 1980s it had taken on extended senses in sociology, e.g.: "allocating benefits in various policy fields in such a way as to provide groups, persons, and places with at least a minimum level of benefits so as to satisfy basic needs" [Stuart S. Nagel, "Equity as a Policy Goal," 1983].
mid-12c., "the exercise of authority in vindication of right by assigning reward or punishment;" also "quality of being fair and just; moral soundness and conformity to truth," from Old French justice "justice, legal rights, jurisdiction" (11c.), from Latin iustitia "righteousness, equity," from iustus "upright, just" (see just (adj.)).
Justice is the end of government. It is the end of civil society. It ever has been and ever will be pursued until it be obtained, or until liberty be lost in the pursuit. ["The Federalist," No. 51]
Meaning "right order, equity, the rewarding to everyone of that which is his due" in English is from late 14c. The Old French word had widespread senses including also "uprightness, equity, vindication of right, court of justice, judge." In English c. 1400-1700 sometimes also with a vindictive sense "infliction of punishment, legal vengeance." As a title for a judicial officer, c. 1200. Justice of the peace is attested from early 14c. To do justice to (someone or something) "deal with as is right or fitting" is from 1670s. In the Mercian hymns, Latin iustitia is glossed by Old English rehtwisnisse.
Middle English doome, from Old English dom "a law, statute, decree; administration of justice, judgment; justice, equity, righteousness," from Proto-Germanic *domaz (source also of Old Saxon and Old Frisian dom, Old Norse domr, Old High German tuom "judgment, decree," Gothic doms "discernment, distinction"), perhaps from PIE root *dhe- "to set, place, put, do" (source also of Sanskrit dhaman- "law," Greek themis "law," Lithuanian domė "attention").
Originally in a neutral sense but sometimes also "a decision determining fate or fortune, irrevocable destiny." A book of laws in Old English was a dombec. Modern adverse sense of "fate, ruin, destruction" begins early 14c. and is general after c. 1600, from doomsday and the finality of the Christian Judgment. Crack of doom is the last trump, the signal for the dissolution of all things.
Old English swat "perspiration, moisture exuded from the skin," also "labor, that which causes sweat," from Proto-Germanic *swaitaz "sweat" (source also of 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" (source also of 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 Genesis iii.19. Sweat equity is from 1968. Colloquial no sweat "no problem" is attested by 1953, said to be originally U.S. military jargon from the Korean War.
The universal and all-inclusive word today is "sweat." It covers just about everything: "no sweat" means no trouble, no cause for worry, nothing fouled up, don't fret. "It's a sweat" means a patrol looks tough, or an order to dig some more trench is an outrage, or simply that everything is messed up as usual. ["A Frontline Picture No Camera Could Get," Life magazine, March 16, 1953]