The root and words for “six” remained very similar throughout Tolkien’s life. The earliest form of this root was ᴱ√ENE “six” from the Qenya Lexicon of the 1910s, with the derivative ᴱQ. ende “six” (QL/35). In the Early Qenya Grammar of the 1920s, the Qenya word for “six” became ᴱQ. enqe [enkwe] with variant enekse (PE14/49, 82), implying a primitive base ✱enek-. This primitive form was made explicit in The Etymologies of the 1930s, where the root was given as ᴹ√ENEK “six” with derivatives ᴹQ. enqe and N. eneg (Ety/ÉNEK). The root and its derivatives retained this form thereafter.
Tolkien spent a fair amount of time analyzing the origin of this root and the basis for the Q. addition of w in various notes on Elvish numbering systems written in 1968 (VT41, VT42, VT47, VT48). One connection Tolkien regularly made was between √ENEK “six” and √ENED “middle”, as “six” was the “middle” of the duodecimal system of numbering (VT41/16; VT48/9); in this respect it was probably an elaboration of the root √NEK “divide, separate, part” by analogy with √ENED (VT47/16; VT48/9). The Quenya -we may have been either a dual suffix based on “six” as twice three (VT48/10) or it might have been by analogy with other important duodecimal numbers like Q. minquë “eleven” and Q. yunquë “twelve” (48/7). Personally I find the second theory more compelling.