This root first appeared as ᴹ√SED “rest” in The Etymologies of the 1930s with derivatives like ᴹQ. sére “rest, repose, peace” and N. sîdh “peace”, along with the name of the Valië ᴹQ. Este < ᴹ✶ezdē (Ety/SED). The root √SED “rest” along with the etymology of Este reappeared in both the Outline of Phonetic Development (OP1) from the 1930s (PE19/45) and the Outline of Phonology (OP2) from the early 1950s (PE19/92), and again in revisions to the OP2 page annotated in green ink and thus probably from 1970 (PE19/91 and note #110).
The root √SED “rest” was mentioned a couple times in the Quenya Verbal System of the 1940s as the basis for the verb ᴹQ. ser- “rest, repose” (PE22/102, 125) and again (unglossed) in the Quendi and Eldar essay of 1959-60 as the basis for Este (WJ/403). In the sense “peace” this root had some competition, however. In the first version of the Gloria in Excelsis Deo prayer from the mid-1960s, Tolkien used Q. sívë for “peace”, revised to Q. sérë in the second version and then Q. rainë (VT44/32). The word Q. sívë “peace” reappeared in unpublished etymological notes from 1969 derived from the root √SIB “rest, quiet” (VT44/35).
Neo-Eldarin: For purpose of Neo-Eldarin, I would use √SED for the act of resting and so Q. sérë “peace” = “restfulness (personal peace)”, and would use √SIB = “quiet, ✱stillness, absence of activity” and so Q. sívë “peace” = “absence of activity or violence (environmental peace)”. I would use Q. rainë as “good will” in connection to √RAY “smile”.
The early existence of this root was indicated in the Gnomish Lexicon of the 1910s as (unglossed) ᴱ✶haw- where it was the basis of words like G. hau- “to lie” and G. haus “bed” (GL/48). It reappeared in The Etymologies of the 1930s as ᴹ√KHAW “rest, lie at ease”, this time with both Quenya and Noldorin derivatives such as ᴹQ. hauta- “cease, take a rest, stop” and N. haust “bed” (Ety/KHAW). In The Etymologies Tolkien also said this root influenced the meaning of N. hauð “mound” so that it came to mean “grave, tomb” as well (Ety/KHAG, KHAW).
The root reappeared again in revisions made to the Outline of Phonology (OP2) around 1959 with a new gloss “cover up, hide away, lay in store”, along with an extended root √KHAWAD “store, hoard” that continued to influence S. haudh “(funeral) mound” (PE19/91). The root √KHAW >> √KHAWA also appeared in a page of roots having to do with “large and small” of unclear date (but probably late 1950s or early 1960s), with the derivatives Q. höa “big, large” and Q. haura “huge” (PE17/115).
Neo-Eldarin: For purposes of Neo-Eldarin, I think the 1930s meaning “rest, lie at ease” is probably most useful, and I would limit the meaning “lay in store” to its extended root √KHAWAD. As for the meaning “big”, I would limit it to (Quenya-only) Q. höa.