An Etymological Dictionary of the German Language/Annotated/Wiege
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Wiege, feminine, ‘cradle,’ from the equivalent Middle High German wige, wiege, Old High German wiga (*wiega?), and, with a different gradation, waga, feminine; corresponding to Dutch wieg, Old Icelandic vagga, ‘cradle’ (in Anglo-Saxon cradol, English cradle). It is evidently connected with the root weg in bewegen, wackeln; yet some difficulties still remain; the relation of Old High German and Middle High German ie, i, a, is not quite clear (see schief and Stiege).