Squeeze
mid 16th century: from earlier squise, from obsolete queise, of unknown origin.
wiktionary
From earlier squize, squise (whence also dialectal English squizzen and squeege), first attested around 1600, probably an alteration of quease (which is attested since 1550), from Middle English queisen(“to squeeze”), from Old English cwēsan, cwȳsan(“to crush, squeeze”), of unknown origin, perhaps imitative (compare Swedish qväsa, kväsa(“to squeeze, bruise, crush; quell”), Dutch kwetsen(“to injure, hurt”), German quetschen(“to squeeze”)). Compare also French esquicher from Old Occitan esquichar(“to press, squeeze”). The slang expression "to put the squeeze on (someone or something)", meaning "to exert influence", is from 1711. The baseball term "squeeze play" is first recorded 1905. "Main squeeze" ("most important person") is attested from 1896, the specific meaning "one's sweetheart, lover" is attested by 1980.
The nonstandard strong forms squoze and squozen, attested dialectally since at least the mid-19th century, are by analogy with freeze.
etymonline
squeeze (v.)
c. 1600, "press forcibly" (transitive), probably an alteration of quease (c. 1550), from Old English cwysan "to squeeze," of unknown origin, perhaps imitative (compare German quetschen "to squeeze"). Perhaps altered by influence of many words of similar sense in squ-. Intransitive sense from 1680s. Baseball squeeze play first recorded 1905. The 1811 Dictionary of the Vulgar Tongue has squeeze-crab "A sour-looking, shrivelled, diminutive fellow."
squeeze (n.)
1610s, "act of squeezing," from squeeze (v.). Main squeeze "most important person" is attested from 1896; meaning "one's sweetheart, lover" is attested by 1980. Slang expression to put the squeeze on (someone or something) "exert influence on" is from 1711.