A root for “centre, middle”, it first appeared in The Etymologies of the 1930s as ᴹ√NED with augmented form ᴹ√ENED (Ety/ÉNED, NÉD). The only derivative of its unaugmented form was the Noldorin prefix N. nedh- “mid-”; its usual forms N. enedh/ᴹQ. ende were derived from the augmented form ᴹ√ENED. In notes from the 1950s and 60s, it seems this augmented form became the normal form, as in √EN(ED) “center, middle” (PE17/26) or ened- “middle” (VT47/26).
One complication in the later iterations of the root was the appearance of the word S. Enedwaith “Middle-region” in The Lord of the Rings maps and appendices (LotR/1089). I suspect this form dates from the period in Lord of the Rings drafts of the 1940s where Tolkien decided to represent [ð] as d: compare N. Fanuidol (TI/306) vs. S. Fanuidhol (LotR/283) and N. Galadrim (TI/239) vs. S. Galadhrim (LotR/341). For whatever reason, Enedwaith was never corrected, and in some places Tolkien said this was a mistake and the proper form should be Enedhwaith (PM/328; VT42/20) while in other places he considered revising the root for “middle” to √ENET or √HEN(ET) (VT41/16).
In his notes on numbers and fingers from 1968, Tolkien said the primitive form was ened with variant form enel (VT47/16, 29; VT48/9-10, 24-25), as the result of frequent d/l interchange in Common Eldarin (VT47/29). In these notes this “middle” root was likewise connected to √ENEK “three” as represented by the “middle” finger (VT48/10). In this set of 1968 notes Tolkien also said √ENET was connected to the distinct root √EN “again” and had the sense “one more” (VT47/15; VT48/25). As for the enel “middle” variant, it seems it was used more in Nandorin (VT47/29), but was a factor in some Quenya words such as Q. enelmo “go-between, intervener, intermediary, mediator” (VT47/14).
Neo-Eldarin: For purposes of Neo-Eldarin, I think it is best to assume the root for “middle” was mainly √ENED, and that Tolkien’s flirtations with √(H)ENET “middle” was a transient idea. I think it is also worth retaining the unaugmented prefix nedh- “mid-” for Neo-Sindarin words, though originating from a lost original vowel rather than a lack of augmentation.
This root served as the basis for Elvish words for “three” for much of Tolkien’s life. However, in its earliest appearance in the Qenya Lexicon of the 1910s, ᴱ√NELE was glossed “point” with derivatives like ᴱQ. neldor “beech”, ᴱQ. nele “tooth” and ᴱQ. nelt “corner”, while the derived numeral was ᴱQ. nelde “four” (QL/65). The contemporaneous Gnomish Lexicon also had G. nel “point, end, tip, jutting end” (GL/60), and G. deldron “beech” was almost certainly derived from a strengthened form of the root ndel- (PE11/8; GL/30). ᴱQ. nelde “three” first appeared in the Early Qenya Grammar of the 1920s (PE14/49, 82).
In the first layer of The Etymologies of the 1930s, this root was glossed “point, triangle” (EtyAC/NEL), but Tolkien changed the gloss of ᴹ√NEL to “three” and gave it two extended roots ᴹ√NELED (also “three”) and ᴹ√NELEK “tooth” (Ety/NEL, NELEK). In this revised paradigm, probably “tooth” was derived from the sense “triangle”. In The Etymologies of the 1930s, Ilk. neldor “beech” was still derived from this root, but was said to refer to the “three trunks” of Hirilorn.
In later writings from the 1950s and 60s, the gloss of √NEL was consistently “three” (WJ/421; VT42/24; VT47/10-11), and the extended form √NELED “three” appeared regularly as well (VT42/24; VT47/11). √NELEK “tooth” also appeared in several documents from the 1940s and 50s (PE19/58; PE21/56, 71).