Other forms: wags, wagging, wagged
To wag is to move something back and forth, the way a dog's tail does. Quick, repeated, side to side.
Tails are the main thing that wags, and a wagging tail is the standard sign of a happy dog. Fingers wag too, in disapproval, and so do tongues, since tongues wagging means people are gossiping. There is an old and entirely separate noun, since a wag is a person who makes jokes, which survives mainly in the phrase some wag had written on the sign. The past tense doubles the g, giving wagged.
Proto-Germanic
*wagōną — to wag
Old Norse
vaga — to wag, waddle
Old English
wagian — to wag, wave, shake
Middle English
waggen
English, today
wag
From Middle English waggen, probably from Old English wagian (“to wag, wave, shake”) with reinforcement from Old Norse vaga (“to wag, waddle”); both from Proto-Germanic wagōną (“to wag”). Related to English way. The verb may be regarded as an iterative or emphatic form of a doublet of waw, which is often nearly synonymous; it was used, e.g., of a loose tooth. Parallel formations from the same root are the Old Norse vagga feminine, cradle (Swedish vagga, Danish vugge), Swedish vagga (“to rock a cradle”), vugge (“to rock a cradle”), Dutch wagen (“to move”), early modern German waggen (dialectal German wacken) to waver, totter. Compare waggle, verb
Etymology from Wiktionary, CC BY-SA