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 1940s (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 (QVS) from 1948 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 The word Q. sívë “peace” reappeared in unpublished etymological notes from 1969 derived from the root √SIB “rest, quiet” (VT44/35).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 purposes 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” probably from around 1968 (VT47/26 note #26), 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.