Old English -stoppian (in forstoppian "to stop up, stifle"), a general West Germanic word, cognate with Old Saxon stuppon, West Frisian stopje, Middle Low German stoppen, Old High German stopfon, German stopfen "to plug, stop up," Old Low Frankish (be)stuppon "to stop (the ears)."
These words are said by many sources to be a Germanic borrowing of Vulgar Latin *stuppare "to stop or stuff with tow or oakum" (source of Italian stoppare, French étouper "to stop with tow"), from Latin stuppa "coarse part of flax, tow." In support of this theory, it is said that plugs made of tow were used from ancient times in Rhine valley. Century Dictionary says this "suits phonetically," but "is on grounds of meaning somewhat doubtful." Barnhart, for one, proposes the whole Germanic group might be native, from a base *stoppon.
Sense of "bring or come to a halt, discontinue" (mid-15c.) is from notion of preventing a flow by blocking a hole, and the word's development in this sense is unique to English, though it since has been widely adopted in other languages; perhaps influenced by Latin stupere "be stunned, be stupefied." Intransitive meaning "check oneself" is from 1680s. Meaning "make a halt or stay, tarry" is from 1711. Stop-light is from 1922; stop-sign is from 1918. Stop-motion is from 1851, originally of looms. Related: Stopped; stopping.