This root first appeared as ᴹ√KHEN “look at, see, observe, direct gaze” with an extended form ᴹ√KHEN-D-E “eye” in The Etymologies of the 1930s, with derivatives ᴹQ. hen (hend-) and N. hên “eye” (Ety/KHEN-D-E, EtyAC/KHEN).
The derived forms arose earlier, with ᴱQ. hen “eye” appearing in The Qenya Phonology of the 1910s, but there it was a derivative of ᴱ√þeχe > þχe-ndǝ > hen (PE12/21). Indeed, the majority of the derivatives of this early root show s- in Qenya, and the root was given as ᴱ√SEHE or ᴱ√SE’E in the Qenya Lexicon of the 1910s (QL/82). Contemporaneous forms in the Gnomish Lexicon such as G. thê- “see” and G. thest “sight” (GL/72), but G. sî “bead, small gem or pearl” may also be related, perhaps indicate a blending between ᴱ√SEHE and ᴱ√ÞEHE [þeχe].
The word G. hen “eye” also appeared in the Gnomish Lexicon (GL/48), probably with an origin similar to ᴱQ. hen, and these two words reappeared in Early Noldorin word lists from the 1920s, but as a derivative of ✶ske-ndá (PE13/147). Thus it seems the initial combination evolved from the 1910s þχ- >> 1920s sk- >> 1930s kh-. In the 1930s, the base root ᴹ√KHEN meant “see”, but Tolkien established a distinct root √KEN “see” by the 1940s (PE22/103), and in notes from 1955 Tolkien described √KHEN as “base of eyewords” without mentioning sight (PE17/187).
A primitive suffixal form appearing in Common Eldarin: Noun Structure and serving as the basis of feminine words, most notably the femininizing suffixes -ī and -ē and “adjectival” ✶yenā (PE21/82-83) (PE21/82-83). A similar set of ancient feminine suffixes appeared in the first version of notes on Quenya Personal Pronouns (QPP1) from the late 1940s (PE23/87), and again in notes on Eldarin Pronouns, Demonstratives, and Correlatives (EP1) from the early 1950s (PE23/129). For most purposes of Neo-Eldarin, I think it is best to limit this root to suffixes.