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mid-13c., from Old English sweostor, swuster "sister," or a Scandinavian cognate (Old Norse systir, Swedish syster, Danish søster), in either case from Proto-Germanic *swestr- (cf. 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 PIE root words, recognizable in almost every modern Indo-European language (e.g. Sanskrit svasar-, Avestan shanhar-, Latin soror, Old Church Slavonic, Russian sestra, Lithuanian sesuo, Old Irish siur, Welsh chwaer, Greek eor). French soeur "a sister" (11c., instead of *sereur) is directly from Latin soror, a rare case of a borrowing from the nominative case.
According to Klein's sources, probably from PIE roots *swe- "one's own" + *ser- "woman." For vowel evolution, see bury. Used of nuns in Old English; of a woman in general from 1906; of a black woman from 1926; and in the sense of "fellow feminist" from 1912. Meaning "female fellow-Christian" is from mid-15c. Sister act "variety act by two or more sisters" is from vaudeville (1908).