This root was used for Elvish words for “white” and “snow” for much of Tolkien’s life. It first appeared as ᴱ√NIQI “white” in the Qenya Lexicon of the 1910s with derivatives like ᴱQ. niqis “snow” and ᴱQ. ninqe “white” (QL/66), the latter surviving more or less unchanged for the rest of Tolkien’s life. In the contemporaneous Gnomish Lexicon it had derivatives like G. nictha- “to rain, hail, snow” and G. nimp “pallid” (GL/60), the latter the cognate of ᴱQ. ninqe and another word that survived in Tolkien’s later conceptions of the languages.
The root appeared as unglossed ᴹ√NIK-W in The Etymologies, again with ᴹQ. ninqe “white” and N. nimp “pale” and other similar words, including ᴹQ. niqe “snow” (Ety/NIK-W). The root was mentioned again in Tolkien’s later writing as √NIK-W (PE17/160) or √NIK (PE17/168) as a basis for “snow” words. In Sindarin Tolkien felt it was influenced by other roots, such as √(N)DIP/B “bending and drooping” (PE17/168) or √NIP “small with a connotation of weakness” (VT48/18) so that S. nimp also took on a connotation of weakness and frailty, and hence was used for “pale, pallid” rather than simply “white”.
One of various roots for “small” Tolkien used in his later writings. The root √NIK “small” first appeared in notes on Eldarin Hands, Fingers and Numerals from the late 1960s (VT47/26; VT48/18), but was connected to the diminutive suffix ✶-i(n)ki which had a much longer conceptual history. One of the earliest known diminutive suffix was ᴱQ. -íne(a) in the Qenya Lexicon of the 1910s from the root ᴱ√INI “small” (QL/42), which might be a precursor to √NIK; these suffixes reappeared in the Early Qenya Grammar of the 1920s (PE14/49, 81). In the Gnomish Grammar of the 1910s, the word G. inc “small” was used as the basis for the “diminutive superlative” -inci (PE11/16).
In the Qenya Lexicon, Tolkien connected ᴱ√INI “small” to the root ᴱ√MINI of similar meaning (QL/42, 61). There are no signs of ᴱ√MINI “small” in the contemporaneous Gnomish Lexicon, but the word G. migin “little” (GL/57) hints at a (hypothetical) variant root ✱ᴱ√MIKI. Further support for ✱ᴱ√MIKI can be found in other diminutive forms in the Early Qenya Grammar of the 1920s such as prefixal diminutive ᴱQ. mike- along adverbial ᴱQ. mike “little” (QL/48, 81), the latter appearing with the gloss “a bit” in the English-Qenya Dictionary from this period (PE15/70) along with other similar words in both the dictionary and the grammar. This ✱ᴱ√MIKI might be another precursor to √NIK. An early hint at √NIK itself might appear in the word ᴹQ. nikse “minnow, little fish” from the Declension of Nouns from the early 1930s (PE21/27).
In Noldorin and Sindarin, the primary diminutive suffix became -eg, which was connected to the Common Eldarin suffix -iki elsewhere in notes on hands and fingers (VT47/14 note #21). In the notes where √NIK “small” appeared in the late 1960s, Tolkien gave the primitive diminutive as -inkĭ along with variants ikki, -iksi, -si, -ensi, -ki.
One of the main competing roots for “small” was ᴹ√PIK [see the entry for √PI(N)], itself with a lengthy conceptual history. The shift of pitya >> nitya “little” in the father name of Amrod from the late 1960s may represent a replacement of √PIK by √NIK (PM/365), but I think it is likelier the two roots coexisted with slightly different meanings, as was the case for their earlier precursors. In the notes from the late 1960s, √NIK was also contrasted with √NIP “small (usually with connotation of weakness)” (VT48/18), from which the word S. niben “petty” was derived, as in S. Nogoth Niben (WJ/388).
Neo-Eldarin: For purposes of Neo-Eldarin, I would assume √NIK meant “small” in a neutral sense, √PIK “tiny” (along with variants √PĪ and √PIN) and √NIP “small and weak”. I would use these as the major Eldarin roots for “small” words, along with a number of other more specialized roots.