Old English wadan "to go forward, proceed, move, stride, advance" (the modern sense perhaps represented in oferwaden "wade across"), from Proto-Germanic *wadanan (source also of Old Norse vaða, Danish vade, Old Frisian wada, Dutch waden, Old High German watan, German waten "to wade"), from PIE root *wadh- (2) "to go," found only in Germanic and Latin (source also of Latin vadere "to go," vadum "shoal, ford," vadare "to wade"). Italian guado, French gué "ford" are Germanic loan-words.
Specifically "walk into or through water" (or any substance which impedes the free motion of limbs) c. 1200. Originally a strong verb (past tense wod, past participle wad); weak since 16c. Figurative sense of "to go into" (action, battle, etc.) is recorded from late 14c. Related: Waded; wading.
Forbade to wade through slaughter to a throne,
And shut the gates of mercy on mankind,
[Gray, from "Elegy Written in a Country Churchyard"]
"watercourse," 1839, from Arabic wadi "seasonal watercourse," prop. participle of wada "it flowed." It forms the Guadal- in Spanish river names.
late 14c., "thin cake of paste, generally disk-shaped," from Anglo-French wafre, Old North French waufre "honeycomb, wafer" (Old French gaufre "wafer, waffle"), probably from Frankish *wafel or another Germanic source (compare Flemish wafer, altered from Middle Dutch wafel "honeycomb;" see waffle (n.)). Eucharistic bread first so called 1550s.
"kind of batter-cake, baked crisp in irons and served hot," 1744, from Dutch wafel "waffle," from Middle Dutch or Middle Low German wafel, from Proto-Germanic *wabila- "web, honeycomb" (source also of Old High German waba "honeycomb," German Wabe), related to Old High German weban, Old English wefan "to weave" (see weave (v.)). Sense of "honeycomb" is preserved in some combinations referring to a weave of cloth. Waffle iron is from 1794.
1690s, "to yelp, bark," frequentative of provincial waff "to yelp, to bark like a puppy" (1610); possibly of imitative origin. Figurative sense of "talk foolishly" (c. 1700) led to that of "vacillate, equivocate" (1803), originally a Scottish and northern English usage. Late 17c. Scottish also had waff "act of waving," variant of waft, which might have influenced the sense. Related: Waffled; waffler; waffling.
c. 1500, transitive, "to move gently" (through the air), probably from Middle Dutch or Middle Low German, ultimately from wachten "to guard" (perhaps via notion of a ship that guards another as it sails), related to waken "rouse from sleep," from Proto-Germanic *waht-, from PIE root *weg- "to be strong, be lively." Possibly influenced by northern dialect waff "cause to move to and fro" (1510s), a variant of wave. Intransitive sense from 1560s. Related: Wafted; wafting.
early 13c. (intransitive), "waver, vacillate, lack steadfastness," probably from a Scandinavian source (compare Old Norse vagga "a cradle," Danish vugge "rock a cradle," Old Swedish wagga "fluctuate, rock" a cradle), and in part from Old English wagian "move backwards and forwards;" all from Proto-Germanic *wag- (source also of Old High German weggen, Gothic wagjan "to wag"), probably from PIE root *wegh- "to go, move, transport in a vehicle."
Transitive meaning "move (something) back and forth or up and down" is from c. 1300; of dogs and their tails from mid-15c.: "and whanne they [hounds] see the hure maystre they wol make him cheere and wagge hur tayles upon him." [Edward, Duke of York, "The Master of Game," 1456]. Related: Wagged; wagging. Wag-at-the-wall (1825) was an old name for a hanging clock with pendulum and weights exposed.