The root √TUL was used for Elvish words having to do with motion towards a speaker for much of Tolkien’s life, but the precise meaning evolved over time. The earliest appearance of this root was as ᴱ√TULU “fetch, bear, bring; move, come”, but with an original sense = “uphold, support, bear, carry” (QL/95). It had a derived verb ᴱQ. tulu- matching the verbal sense of the root along with an added sense “produce, bear fruit”, but it had other derivatives like ᴱQ. tulma “bier, tray” and ᴱQ. tulwe “tall thin pillar, standard, pole; banner” connected to the older “support” sense of the root. It had a similar divergence of meaning in its derivatives from the contemporaneous Gnomish Lexicon, such as G. taul “a pillar” vs. G. tul- “bring; come to” (GL/69, 71). This 1910s root ᴱ√TULU may also have been connected to ᴱ√TḶPḶ which likewise had derivatives having to do with “support” (QL/93).
In The Etymologies of the 1930s the root ᴹ√TUL had the gloss “come, approach, move towards (point of speaker)” with derivatives like ᴹQ. tul-/N. tol- “come” and ᴹQ. tulta-/N. toltha- “send for, fetch, summon” = “(orig.) make come” (Ety/TUL); in the 1930s the “support” words seem to have been transferred to (probably unrelated) ᴹ√TULUK. √TUL “come” was mentioned regularly in Tolkien’s later writings (PE22/103; PE17/188; PE22/156), in one 1969 note with the extra gloss “approach” (PE22/168), so the 1930s senses for the root seem to have been retained thereafter.
The root √KOL served various purposes throughout Tolkien’s life. The root appeared as two separate entries in the Qenya Lexicon of the 1910s: ᴱ√KOLO “to strain through” and also as ᴱ√KOLO, unglossed but with derivatives like ᴱQ. koli- “to prick”, ᴱQ. kolme “point, tip”, and ᴱQ. kolman “peak, summit”, so perhaps meaning something like “✱point” (QL/47). It reappeared in a rejected entry in The Etymologies of the 1930s as ᴹ√KOL with a single derivative ᴹQ. kolma “ring”, and the root had the gloss “round, (?rim)” in an earlier version of the entry (EtyAC/KOL). It had a deleted reference in the entry ᴹ√KOR “round” of which it was probably a variant (EtyAC/KOR).
The root √KOL appeared regularly in Tolkien’s writing in the 1950s and 60s with glosses like “bear, carry” and derivatives of similar meaning (PE17/145, 158; PE22/152, 155; VT39/10). This new meaning of the root was anchored in the words Q. colindo “bearer” as in Q. Cormacolindor “Ring-bearers” (LotR/953), as well as S. coll “cloak” in S. Thingol “Grey-cloak” (PE17/72). In notes from 1969, Tolkien clarified that the root referred “to the ability to support weight or a burden, physical or mental, not necessarily to transporting it” (PE22/155).