Old English stæger "stair, flight of steps, staircase," from Proto-Germanic *staigri (source also of Middle Dutch stegher, Dutch steiger "a stair, step, quay, pier, scaffold;" German Steig "path," Old English stig "narrow path"), from PIE *steigh- "go, rise, stride, step, walk" (source also of Greek steikhein "to go, march in order," stikhos "row, line, rank, verse;" Sanskrit stighnoti "mounts, rises, steps;" Old Church Slavonic stignati "to overtake," stigna "place;" Lithuanian staiga "suddenly;" Old Irish tiagaim "I walk;" Welsh taith "going, walk, way"). Originally also a collective plural; stairs developed by late 14c.
well n.
"hole dug for water, spring of water," Old English wielle (West Saxon), welle (Anglian) "spring of water, fountain," from wiellan (see well (v.)). "As soon as a spring begins to be utilized as a source of water-supply it is more or less thoroughly transformed into a well" [Century Dictionary]. Figurative sense of "source from which anything is drawn" was in Old English.