An Etymological Dictionary of the German Language/Annotated/Stauche
Stauche, feminine, ‘veil, sleeve, muff, mitten,’ from Middle High German stûche, Old High German stûhha, feminine, ‘the broad pendant sleeve on a woman's dress, kerchief, veil, cloth, apron’; corresponding to Anglo-Saxon stocu, ‘long sleeve, Old Icelandic stúka. The Romance cognate, French étui (Italian astuccio), ‘case,’ has been derived rom a Teutonic *stûkjo. Teutonic stū̆kô (stū̆kjo) is usually connected with a pre-Teutonic root stū̆g; Old Low German stûkan, Dutch stuiken, ‘to pile up, push,’ and Lithuanian stùgti, ‘to look aloft.’