"a weaver," Old English webbestre "a female weaver," from web (q.v.) + fem. suffix -ster. Noah Webster's dictionary, typically American and execrable for etymology, was first published 1828.
Entries linking to webster
web n.
Old English webb "woven fabric, woven work, tapestry," from Proto-Germanic *wabjam "fabric, web" (source also of Old Saxon webbi, Old Norse vefr, Dutch webbe, Old High German weppi, German gewebe "web"), from PIE *(h)uebh- "to weave" (see weave (v.)).
Meaning "spider's web" is first recorded early 13c. Applied to the membranes between the toes of ducks and other aquatic birds from 1570s. Internet sense is from 1992, shortened from World Wide Web (1990). Web browser, web page both also attested 1990.
-ster
Old English -istre, from Proto-Germanic *-istrijon, feminine agent suffix used as the equivalent of masculine -ere (see -er (1)). Also used in Middle English to form nouns of action (meaning "a person who ...") without regard for gender.
The genderless agent noun use apparently was a broader application of the original feminine suffix, beginning in the north of England, but linguists disagree over whether this indicates female domination of weaving and baking trades, as represented in surnames such as Webster, Baxter, Brewster, etc. (though modern spinster probably carries an originally female ending).
Also compare whitester "one who bleaches cloth;" kempster (c. 1400; Halliwell has it as kembster) "woman who cleans wool." Chaucer ("Merchant's Tale") has chidester "an angry woman" (the 17c. had scoldster). Also compare Middle English shepster (late 14c.) "dressmaker, female cutter-out," literally "shapester," sleestere (mid-15c.) "murderess, female killer" ("slay-ster"). Sewster "seamstress" (Middle English seuestre, late 13c. as a surname, also used of men) is still in Jonson but was obsolete or provincial after 17c. In Modern English, the suffix has been productive in forming derivative nouns (gamester,roadster,punster, rodster "angler," etc.).
spinster n.
mid-14c., "female spinner of thread," from Middle English spinnen "spin fibers into thread" (see spin (v.)) + -stere, feminine suffix (see -ster). Unmarried women were supposed to occupy themselves with spinning, hence the word came to be "the legal designation in England of all unmarried women from a viscount's daughter downward" [Century Dictionary] in documents from 1600s to early 1900s, and by 1719 the word was being used generically for "woman still unmarried and beyond the usual age for it."
Spinster, a terme, or an addition in our Common Law, onely added in Obligations, Euidences, and Writings, vnto maids vnmarried. [John Minsheu, "Ductor in Linguas," 1617]
Strictly in reference to those who spin, spinster also was used of both sexes (compare webster, Baxter, brewster) and so a double-feminine form emerged, spinstress "a female spinner" (1640s), which by 1716 also was being used for "a maiden lady." Related: Spinsterhood.