Pout
Middle English (as a verb): perhaps from the base of Swedish dialect puta ‘be inflated’. Compare with pout2.
wiktionary
From Middle English pouten, probably from Scandinavian (compare Norwegian pute(“pillow, cushion”), dial. Swedish puta(“to be puffed out”), Danish pude(“pillow, cushion”)), from Proto-Germanic *pūto(“swollen”) (compare English eelpout, Dutch puit, Low German puddig(“inflated”)), from Proto-Indo-European *bu-(“to swell”) (compare Sanskrit बुद्बुद(budbuda, “bubble”)).
From Middle English *poute, from Old English *pūte as in ǣleputa, ǣlepūte(“eelpout”), ultimately from Proto-Indo-European *bew-(“to swell”).
pout (plural pouts)
etymonline
pout (v.)
"thrust out the lips, as in sullenness or displeasure," mid-14c., of uncertain origin, perhaps from Scandinavian (compare Swedish dialectal puta "to be puffed out"), or Frisian (compare East Frisian püt "bag, swelling," Low German puddig "swollen"); related via notion of "inflation" to Old English ælepute "fish with inflated parts," Modern English pout as a fish name, and Middle Dutch puyt, Flemish puut "frog," all from a hypothetical PIE imitative root *beu- suggesting "swelling" (see bull (n.2)). Also compare French bouder "to pout," also presumably imitative (and the source of boudoir). Related: Pouted; pouting.
As a noun from 1590s; "a protrusion of the lips as in pouting; a fit of sullenness or displeasure."