The word cloud comes from old English clud "mass of rock, hill," apparently from the similarity of storm clouds to hills. Sky, from Old Norse sky, also means "cloud."
What about those fancy Latin names? According to Etymology online, they were thought up by British amateur meteorologist Luke Howard in 1802.
Cirrus is Latin for "curl-like tuft, ringlet of hair." The meteorological term is related to the shape of the clouds.
Cumulus means "a heap, a pile, mass" in Latin. That's a pretty good description of cumulus clouds.
The word for a thin layer of cloud, stratus, comes from Latin sternere, to spread out. It means "a thing spread out, horse-blanket, coverlet."
The word nimbus is from the 1600s, meaning a bright cloud surrounding a god. It comes from the Latin nimbus, "cloud."
Bonus: Nebula, Latin for "cloud, mist, vapor, fog, exhalation," has a sinister figurative meaning of "darkness, obscurity." The astronomical term "cloud-like patch in the night sky" is from the 1700s.