From Middle English swith, from Old English swīþ (“strong, mighty, powerful, active, severe, violent”), from Proto-Germanic *swinþaz (“strong”), from Proto-Indo-European *swento- (“active, healthy”). Cognate with Old Saxon swīth, Middle High German swind (Modern German geschwind (“fast, quick, swift”)), Middle Low German swīde (Modern Low German swinn (“fast, quick, swift”) through High German influence), Dutch gezwind (“fast, quick, swift”), Old Norse svinnr, Gothic 𐍃𐍅𐌹𐌽𐌸𐍃 (swinþs, “strong”). Related to sound.
From Middle English swith, swithe, from Old English swīþe (“very much, exceedingly, severely, violently, fiercely”), from Proto-Germanic *swinþa (“strongly”), from Proto-Indo-European *swento- (“active, healthy”). Not cognate to superficially similar swift, as these have distinct PIE roots, though both share *swe- prefix in PIE.