sister-in-law (n.)

mid-13c., suster, "female sibling, a female person in her relation to other children of the same parents," from Old English sweostor, swuster, Northumbrian soester "sister," or a Scandinavian cognate (Old Norse systir, Swedish syster, Danish søster), in any case from Proto-Germanic *swestr- (source also of Old Saxon swestar, Old Frisian swester, Middle Dutch suster, Dutch zuster, Old High German swester, German Schwester, Gothic swistar).

These are from PIE *swesor, one of the most persistent and unchanging root words, recognizable in almost every modern Indo-European language (Sanskrit svasar-, Avestan shanhar-, Latin soror, Old Church Slavonic, Russian sestra, Lithuanian sesuo, Old Irish siur, Welsh chwaer). Greek eor "daughter, cousin" is the surviving relic of the root in that language, perhaps from a dialectal vocative form; it was replaced as "sister" byadelphē (for which see Adelphi).French soeur "a sister" (11c., instead of *sereur) is directly from Latin soror, a rare case of a borrowing from the nominative case.

The forms in -u- persisted through Middle English; for the vowel evolution, see bury. It was used of nuns in Old English, of the Fates from c. 1300, the Muses from late 14c., and of the Pleiades from early 15c.

From late 14c. as "fellow woman," without regard to relationship, "fellow creature, woman sharing the human condition," also "woman engaged in the same activity as another." The meaning "female fellow-Christian, woman of one's own faith" is from mid-15c. In modern use, of a woman in general from 1906; especially in U.S. of "a Black woman" from 1926; and in the sense of "fellow feminist" from 1912. Sister act "variety act by two or more sisters" is from vaudeville (1908).

1894, "anyone of a relationship not natural," abstracted from father-in-law, etc.

The position of the 'in-laws' (a happy phrase which is attributed ... to her Majesty, than whom no one can be better acquainted with the article) is often not very apt to promote happiness. [Blackwood's Magazine, 1894]

The earliest recorded use of the formation is in brother-in-law (13c.); the law is Canon Law, which defines degrees of relationship within which marriage is prohibited. Thus the word originally had a more narrow application; its general extension to more distant relatives of one's spouse is, according to OED "recent colloquial or journalistic phraseology." Middle English inlaue (13c.) meant "one within or restored to the protection and benefit of the law" (opposite of an outlaw), from a verb inlauen, from Old English inlagian "reverse sentence of outlawry."