Bάλλω combined with παρα "beside" to form παραβάλλω "to throw beside; compare". Παραβολή meant "comparison, analogy; parable", borrowed into Latin as parabola. This became Old French parable, and also parler "speech" and parlement "discussion, meeting". The -ia- spelling of parliament has not been fully explained (OED).
The OED says in the entry for bale "to dance":
a. OF. baler (since 16th c. baller) to dance (= Pr. balar, It. ballare, Sp., Pg. bailar):-late L. (Isidore) ballāre to dance. Some think the L. formed from Gr. βαλλίζειν to dance, some f. balla BALL n.1, on the alleged ground that, in the Middle Ages, tennis was accompanied with dancing and song.
The AHD claims that βαλλίζω "to dance, jump about" is derived from βάλλω "to throw", so words like ballad, ballet and ball "a formal gathering for social dancing" are ultimately from *gʷelh₁-.
In English, *gʷelh₁- became cwellan "to kill, destroy" and quell.