Weave
Old English wefan, of Germanic origin, from an Indo-European root shared by Greek huphē ‘web’ and Sanskrit ūrṇavābhi ‘spider’, literally ‘wool-weaver’. The current noun sense dates from the late 19th century.
wiktionary
From Middle English weven(“to weave”), from Old English wefan(“to weave”), from Proto-West Germanic *weban, from Proto-Germanic *webaną, from Proto-Indo-European *webʰ-(“to weave, braid”).
From Middle English weven(“to wander”); probably from Old Norse veifa(“move around, wave”), related to Latin vibrare.
etymonline
weave (v.1)
Old English wefan "to weave, form by interlacing yarn," figuratively "devise, contrive, arrange" (class V strong verb; past tense wæf, past participle wefen), from Proto-Germanic *weban (source also of Old Norse vefa, Middle Low German, Middle Dutch, Dutch weven, Old High German weban, German weben "to weave"), from PIE root *(h)uebh- "to weave;" also "to move quickly" (source also of Sanskrit ubhnati "he laces together," Persian baftan "to weave," Greek hyphē, hyphos "web," Old English webb "web").
The form of the past tense altered in Middle English from wave to wove. Extended sense of "combine into a whole" is from late 14c.; meaning "go by twisting and turning" is from 1640s. Related: Wove; woven; weaving.
weave (n.)
1580s, "something woven," from weave (v.). Meaning "method or pattern of weaving" is from 1888.
weave (v.2)
c. 1200, "to move from one place to another," of uncertain origin, perhaps from weave (v.1). From early 14c. as "move to and fro;" 1590s as "move side to side." Use in boxing is from 1818. Related: Weaved; weaving.