This root appeared in various notes from the late 1960s as the basis for the particle of uncertainty Q. cé. This particle meant “if” or “maybe” in various contexts, but in notes from 1969 √KE was given the sense “may (be)” and paired with √KWI “suppose”, which was the basis for qui “if” (PE22/158). This can be compared to another paradigm also from 1969 associated with the Ambidexters Sentence where cé meant “if” and it seems the root √keye (with derived verb cíta-) meant “suppose” (VT49/19). Of the two paradigms, I think √KE “maybe”/√KWI “if, suppose” is more useful for the purposes of Neo-Eldarin, but it seems Tolkien’s own thoughts on the subject were in flux.
In notes written in 1967, Tolkien gave what was apparently an inverted form of this root, √ek “it is open”, from which the impersonal Quenya verb ec- “may, can” in the sense “have the opportunity to” is derived (VT49/20). This inverted form is almost certainly related to √KE, as suggested by Patrick Wynne.
The root √EK was associated with pointed things for all of Tolkien’s life. It first appeared as the root ᴱ√EKE with variant ᴱ√EHE [eχe] in the Qenya Lexicon of the 1910s (QL/35), and as eke and eχe in the contemporaneous Gnomish Lexicon where Tolkien made it clear it was the blending of two roots of similar meaning (GL/31). In the Gnomish Lexicon it had a third variant aχe, but Tolkien seemed less certain of that variant. In the 1910s and 1920s it was the basis for words meaning “sword”, “spear” and “thorn”.
By the 1930s, the sword-words had fallen away, transferred to ᴹ√MAK. The root ᴹ√EK appeared in The Etymologies of the 1930s with the gloss “spear”, but I believe that gloss applied only to its extended form ᴹ√EKTE/EKTI; in rough notes from the 1940s ᴹ√EK was glossed “point, sharp point, thorn” (PE22/127). The primitive form eke appeared in the Quendi and Eldar essay from 1959-1960 with the gloss “sharp point”, and √EK appeared again in etymological notes from 1968 with this same gloss (VT48/25). Thus this root seems to have been very well established in Tolkien’s mind as the basis for pointy things.