From Middle English stoppen, stoppien, from Old English stoppian, from Proto-West Germanic *stuppōn, from Proto-West Germanic *stoppōn, *stuppijaną, from Proto-Indo-European *(s)tewp-, *(s)tewb-, from *(s)tew-. Cognate with Saterland Frisian stopje ("to stop, block"), West Frisian stopje ("to stop"), Dutch stoppen ("to stop"), Low German stoppen ("to stop"), German stopfen ("to be filling, stuff"), German stoppen ("to stop"), Danish stoppe ("to stop"), Swedish stoppa ("to stop"), Icelandic stoppa ("to stop"), Middle High German stupfen, stüpfen. More at stuff, stump.
Alternate etymology derives Proto-West Germanic *stoppōn from an assumed Vulgar Latin *stūpāre, *stuppāre, from stūpa, stīpa, stuppa, from Ancient Greek στύπη, στύππη. This derivation, however, is doubtful, as the earliest instances of the Germanic verb do not carry the meaning of "stuff, stop with tow". Rather, these senses developed later in response to influence from similar sounding words in Latin and Romance.
From Middle English stoppe, from Old English stoppa ("bucket, pail, a stop"), from Proto-Germanic *stuppô ("vat, vessel"), from Proto-Indo-European *(s)teub- ("to push, hit; stick, stump"). See stoup.
Cognate with Norwegian stopp, stoppa, Middle High German stubech, stübich (German Stübchen). Related also to Middle Low German stōp ("beaker, flask"), Middle High German stouf ("beaker, flask"), Norwegian staupa ("goblet"), Icelandic staupa ("shot-glass"), Old English stēap ("a stoup, beaker, drinking vessel, cup, flagon"). Cognate to Albanian shtambë ("amphora, bucket").