Qenya
vil-
verb. to fly, to fly, [ᴱQ.] float, sail
wil- Archaic
verb. to fly
There are more words but they are from Tolkien's earlier conceptional periods. Tolkien likely changed these words as he evolved the aesthetics and completeness of the languages. You may even find languages that Tolkien later rejected. Do not mix words from different time periods unless you are familiar with the phonetic developments.
Below: Tolkien's Late Period (1950–1973). These are from Tolkien's late conceptual period — his most settled forms of the languages. Prefer these over the earlier ones above when composing new text.
A verb given as {vilin >>} wilin “I fly” in The Etymologies of the 1930s under the root ᴹ√WIL “fly, float in air” (Ety/WIL). Tolkien gave a past form ville that was allowed to stand even after {vilin >>} wilin.
Conceptual Development: The Qenya Lexicon of the 1910s had ᴱQ. ’wili- “sail, fly, float” under the early root ᴱ√GWILI (QL/104). The contemporaneous Gnomish Lexicon had ᴱQ. vil- as the cognate to G. gwil- “sail, float, fly” (GL/45).
Neo-Quenya: For purposes of Neo-Quenya, I would use the form vil- “to fly” in keeping with the general principle that *w* was pronounced and spelt *v* in modern Quenya; see the entry for [w] for discussion. For “sail, float” I would use other verbs such as lut-.