withe

From Middle English withe, from Old English wiþþe (“band, tie”), from Proto-Germanic *wiþiz, *wiþjǭ (“cord, rope”), from Proto-Indo-European *wéh₁itis (“that which twines”), from *weyt- (“that which winds or bends, branch, switch”), from Proto-Indo-European *wey- (“to turn, wind, bend”).

The brickwork and chimney architecture senses may have a different etymology, see wythe.