The earliest iteration of this root was ᴱ√VAẎA “enfold, wind about” from the Qenya Lexicon from the 1910s with derivatives like ᴱQ. vaile “covering”, ᴱQ. vaima “wrap, robe”, and ᴱQ. vaita- “wrap” (QL/100). The contemporaneous Gnomish Lexicon had derivatives like G. baidha- “clothe”, G. bail “sheath, case, cover; pod”, and G. bain “clad”, based on the primitive form Baʒ̔- (GL/21). This likely meant the medial consonant of the root was actually the voiced palatal spirant [ʝ], which Tolkien generally represented as ẏ in Qenya roots (PE12/15-16).
{ᴱN. bain >>} ᴱN. bai “clad” and ᴱN. bail “sheath” from Early Noldorin Word-lists of the 1920s were probably related (PE13/138). In The Etymologies from the 1930s the root appeared as ᴹ√WAY “enfold” with derivatives like ᴹQ. vaita-/N. gwaeda- “enfold” and N. ui “envelope” (Ety/WAY; EtyAC/WAY). In this entry the form was revised to ᴹ√VAY (Ety/WAY). Tolkien also indicated that it was “confused in later Q with BAYA”, perhaps an attempt to salvage the bai- forms of Gnomish and Early Noldorin, but this sentence was struck out and there is no other sign of ᴹ√BAY in The Etymologies.
Neo-Eldarin: In The Etymologies, the Noldorin words for “clothing” seem to have moved to a new root, ᴹ√KHAP “enfold”, but this root had no Quenya derivatives. I think it is best to reconceive of the Early Qenya derivatives of ᴱ√VAẎA related to “clothing” as derivatives of ᴹ√WAY instead. The Gnomish derivatives of ᴱ√VAẎA can’t be easily salvaged, however, since the later roots changed to make it difficult produce their initial b.
A root in The Etymologies of the 1930s glossed “bind” but without derivatives (EtyAC/RAP). The element S. raph (“?rope”) in S. Udalraph “Stirrupless” (“?without (U-) foot-rope”) might be related (UT/313).