1650s, "air-spirit," from Modern Latin sylphes (plural), coined 16c. by Paracelsus, originally referring to any race of spirits inhabiting the air, described as being mortal but lacking a soul. Paracelsus' word seems to be an arbitrary coinage, but perhaps it holds a suggestion of Latin silva and Greek nymph, or Greek silphe "a kind of beetle," but French etymologists propose a Gaulish origin.
The Century Dictionary comments that, "to occultists and quacks like Paracelsus words spelled with -y- look more Greek and convincing." The idea itself seem to have come from the air-spirits of Cabbalism. The meaning "graceful girl" is recorded by 1838, on the notion of "slender figure and light, airy movement" [OED].