The Proto-Indo-European root was *wel- "to turn, to wind, round, curved". This became Old English weliȝ and English willow - the notion of "curved" being applied to the willow's bendable branches. The vowel change from e to i might be due to association with Old English wiliȝe "wicker basket".
The extended form *welw- became Latin volvere "to roll". The prefix ē "out" was added to form ēvolvere "to unroll." This became English evolve and evolution.
Other derivatives include:
waltz from German walzen "to roll, dance the waltz"
helix and helicopter from Greek ἕλιξ heliks "spiral" from the suffixed form *wel-lik-
valley from Old French valee from Latin vallēs, an area surrounded by hills.
whelk from Old English weoloc from Proto-Germanic *weluka- "whelk", so named because of its spiral shell.