"the two protuberances which form the rump in men and animals," c. 1300, probably from Old English buttuc "end, short piece of land," from Proto-Germanic *butaz, from PIE root *bhau- "to strike," thus related to butt (n.1).
"thick end," c. 1400, butte, which probably is related to Middle Dutch and Dutch bot, Low German butt "blunt, dull," Old Norse bauta, from Proto-Germanic *buttan, from PIE root *bhau- "to strike." Or related somehow to Old English buttuc "end, small piece of land," and Old Norse butr "short," from Proto-Germanic *butaz, which is from the same PIE root. Also probably mixed with Old French bot "extremity, end," which also is from Germanic (compare butt (n.3)). The meaning "remainder of a smoked cigarette" is recorded by 1847.