Old English walu "ridge, bank" of earth or stone, later "ridge made on flesh by a lash" (related to weal (n.2)); from Proto-Germanic *walu- (source also of Low German wale "weal," Old Frisian walu "rod," Old Norse völr "round piece of wood," Gothic walus "a staff, stick," Dutch wortel, German wurzel "root"), from PIE root *wel- (3) "to turn, revolve." The common notion perhaps is "raised line." Used in reference to the ridges of textile fabric from 1580s. Wales "horizontal planks which extend along a ship's sides" is attested from late 13c.
round dance performed to music in triple time, extraordinarily popular as a fashionable dance from late 18c. to late 19c., the dance itself probably of Bohemian origin, 1779 (walse, in a translation of "Die Leiden des jungen Werthers" from a French translation, which has walse), from German Waltzer, from walzen "to roll, dance," from Old High German walzan "to turn, roll," from Proto-Germanic *walt- (cognate with Old Norse velta), from PIE root *wel- (3) "to turn, revolve." Described in 1825 as "a riotous and indecent German dance" [Walter Hamilton, "A Hand-Book or Concise Dictionary of Terms Used in the Arts and Sciences"].
The music struck up a beautiful air, and the dancers advanced a few steps, when suddenly, to my no small horror and amazement, the gentlemen seized the ladies round the waist, and all, as if intoxicated by this novel juxtaposition, began to whirl about the room, like a company of Bacchanalians dancing round a statue of the jolly god. "A waltz!" exclaimed I, inexpressibly shocked, "have I lived to see Scotch women waltz?" [The Edinburgh Magazine, April 1820]
surname, early 13c., probably an agent noun from walk (v.) in the sense "to full cloth." preserves the cloth-fulling sense (walker with this meaning is attested from c. 1300). "Walker" or "Hookey Walker" was a common slang retort of incredulity in early and mid-19c. London, for which "Various problematic explanations have been offered" [Century Dictionary].
"Is it?" said Scrooge. "Go and buy it."
"Walk-ER!" exclaimed the boy.
"No, no," said Scrooge. "I am in earnest" (etc.)
[Dickens, "A Christmas Carol"]
1820, from German Walpurgisnacht, witches' revel, especially on the Brocken in the Harz Mountains, on May-day eve, literally "the night of (St.) Walpurgis," from Walburga, English abbess who migrated to Heidenheim, Germany, and died there c. 780; May 1 being the day of the removal of her bones from Heidenheim to Eichstädt.