This root was used for Elvish “fill, full” words for most of Tolkien’s life. The earliest appearance of this root was in the Qenya Lexicon of the 1910s, where it appeared unglossed as ᴱ√QṆTṆ or ᴱ√QATA with derivatives ᴱQ. qanta “full, whole, all” and ᴱQ. qanta- “fill, complete” (QL/78). It seems in this early period, Tolkien favored the root with syllabic Ṇ, given forms ᴱQ. kunta “full” (< ᴱ✶qṇtā́) beside qanta in the Qenya Phonology (PE12/11) and G. cwintha- “to fill” beside G. cwant “full” in the Gnomish Lexicon (GL/28); these vowel variations are indications of syllabic consonants.
In The Etymologies of the 1930s the root appeared as ᴹ√KWAT, mostly with nasal-infixed derivatives like ᴹQ. qanta/N. pant “full”, but with others that were not like N. pathra- “fill” and N. pathred “fullness” (Ety/KWAT). Quenya Personal Pronouns (QPP1) from the late 1940s also had ᴹ√KWAT “fill”, and he said it was possibly related to kwā- “all” (PE23/101). The root appeared in Tolkiens later writings (PE17/68), and in the Quendi and Eldar essay of 1959-60 Tolkien again said it was an extension of the root √KWA (WJ/412), a notion he repeated in notes on numbers from the late 1960s (VT42/24).
A root, frequently but not universally suffixal, indicating completion or fullness. The first appearance of this root was ᴹ√KWA “something” in The Etymologies of the 1930s, serving as the basis for ᴹQ. il-qa “everything, ✱all-thing” (EtyAC/KWA). In notes on Demonstrative, Relative, and Correlative Stems (DRC) from the late 1940s, however, Tolkien’s gave the root a new meaning: kwā- “all”, where it was possibly connected to ᴹ√KWAT “fill” (PE23/101).
√KWA reappeared in the Quendi and Eldar essay of 1959-60 glossed “completion” (WJ/392) or “full” (WJ/412), with extended form √KWAN and the verbal variant √KWAT “fill”. It appeared again in various notes from the late 1960s on numbering systems, glossed “full, complete, all, every” (VT42/24), “whole, complete, all” (VT47/7), or “complete, full, all, the whole” (VT47/17). In these notes it was connected to Tolkien’s latest word for “ten” from this period: ✶kwayam > Q. quean or S. pae. Since the root √IL was usually used for “all, every” in Tolkien’s later writings, I think it is more accurate to attribute the sense “complete(ness)”, “whole(ness)”, or “full(ness)” to √KWA.