I have been thinking lately what the NeoQuenya word for 'weather' could be.
Etymonline gives the origin of the English word as

"O.E. weder, from P.Gmc. *wedran (cf. O.S. wedar, O.N. veðr, O.Fris., M.Du., Du. weder, O.H.G. wetar, Ger. Wetter "storm, wind, weather"), from PIE *we-dhro-, "weather," from root *we- "to blow" (see wind (n.)). Spelling with th first appeared 15c., though pronunciation may be much older.

Weather-beaten is from 1520s. Under the weather "indisposed" is from 1827. Greek had words for "good weather" (aithria, eudia) and words for "storm" and "winter," but no generic word for "weather" until kairos (lit. "time") began to be used as such in Byzantine times. Latin tempestas "weather" (see tempest) also originally meant "time;" and words for "time" also came to mean weather in Irish (aimsir), Serbo-Croatian (vrijeme), Polish (czas), etc."

Of course I could mimic Latin and say lúme means 'weather' by extension but that feels unsatisfactory.

There's an attested Quenya word walwiste "change of mind" (PE17:154) which I think could be used as a model. In this word the wal- element has the meaning of 'emotion', whereas wiste is 'change' (cf. the pair of verbs virya/vista- 'change'. I think 'weather' could be modeled on this, like, say, *vilwiste 'change/turn of air, weather' or *súriwiste 'change of wind, weather', or even *lúmeviste 'change of time, weather' if we go with the tempestas idea.