In Quenya the voiceless velar spirant χ [x] weakened to a simple “breath h”. This weakening happened first at the beginning of words, in the Parmaquesta [PQ] period. It happened later medially, in the Tarquesta [TQ] period. The only combination where the χ was preserved is ht [xt]. Tolkien gave nearly identical descriptions of this change in the Outline of Phonetic Development (OP1) from the 1940s and Outline of Phonology (OP2) from the 1950s. The OP1 description was:

kh: produced a back spirant [χ], as “ch” in Welsh. It was not markedly fronted by adjacent front vowels (e, i), at least no more than the corresponding stop k. During the PQ period this spirant became weakened to breath [h] initially (and initially in the second elements of recognized or loose compounds), but remained a spirant medially ...

In Lindarin also kh became weakened to h (but not lost) medially; except in ht, and in rh, lh. This weakening was very general in all varieties of TQ, but a spirant was usually maintained in ht, rh, lh (Lindarin tt; and rh, lh > rrh, llh, long voiceless r, l) (OP1: PE19/30-31).

In the 1930s, the medial unvoicing was only fully accomplished in the Lindarin dialect, no doubt because the Noldor were familiar with the sound χ in their native Noldorin [pre-Sindarin] language. After Noldorin became Sindarin circa 1950, this was no longer relevant, and the medial change also became universal, as reflected in the description in OP2:

kh became the back spirant [χ], as “ch” in Welsh. It was not markedly fronted by adjacent front vowels ē̆, ī̆, at least no more than the corresponding stop k (or “ck” in English “thick”). In PQ this spirant became weakened to the breath h initially (including the beginnings of the second elements of recognized or loose compounds); but remained a spirant medially ...

In the TQ, also medial [χ], spirantal h, became weakened to breath h. This change was common to all the Valinorean dialects. Again the distinction in spelling was usually maintained, and the learned among the Noldor often restored the pronunciation [χ] for d (or medial h), since that sound was a familiar one (medially) in Sindarin. Note that in certain combinations, dealt with below, such as ht, the weakening to h did not occur (OP2: PE19/71).

It seems spirantal χ lingered longest medially after the liquids l, r, but eventually weakened to produce long voiceless l, r. In the 1930s this was only fully accomplished in Lindarin (see above), but in the 1950s this was a universal change:

[In late (TQ) combinations] long voiceless r, l from older rh, lh (originally = [rχ, lχ]). The spelling was often retained, though [h] ½ was sometimes written for d [χ] (OP2: PE19/82).

Tolkien also mentioned the development of l, r + χ in notes on the Feanorian Alphabet from the 1940s:

Medial lh, rh original = lχ, rχ became ľľ, řř, but the spelling jLd (or jL½), 6Éd (or 7½) was maintained (PE22/45).

Tengwar usage indicates the comparative lateness of the medial χ > h change. In early PQ the tengwa ½ (halla) was used to represent [h] initially (PE19/74); this sound was derived from primitive initial [ɣ] (ʒ) or from preserved primitive [h] in those periods when Tolkien imagined the primitive sound was voiceless. This sound could only appear initially, and after initial χ > h in PQ, the initial [h] of that origin also came to be spelled with ½ to better distinguish it from medial χ [x] (d) which still survived. This was reflected in the revised name of the tengwa d, as described in The Lord of the Rings Appendix E:

Thus No. 11 [d] was called harma when it represented the spirant “ch” in all positions, but when this sound became breath h initially (though remaining medially) the name aha was devised (LotR/1123).

This change in tengwar usage is also mentioned in notes on the Feanor Alphabet from the 1940s:

Initial d [h] = [χ] became already in the classical period breath h. It is thus permissible to use ½ = d initially (only). But the better use is d throughout (PE22/44).

After χ > h medially as well, d was also pronouned [h], except only in the combination ht [xt]. Also note that by the time of TQ, the spelling of initial [h] was switched from halla ½ to hyarmen 9 (PE19/71), perhaps for aesthetic reasons. The end result was that in Quenya tengwar usage the sign d was used for h medially, but the sign 9 was used for h initially; ½ remained principally as a marker of voicelessness.

As discussed above, medial the long voiceless lh, rh could be spelled with either d or ½: lh = jd or j½ and rh = 6d (PQ 7d) or 6½. The spellings with d were the historically correct ones in most cases. The medial spellings with ½ were probably borrowed from the spelling of initial voiceless lh, rh: as noted above, spelling with a preceding or following ½ was often used to represent voiceless sounds in the both the PQ and TQ periods.

Conceptual Development: These same developments happened initially for χ in Early Qenya, as discussed in Qenya Phonology from the 1910s, but medially it was voiced to [ɣ] as was usual for intervocalic voiceless spirants and ultimately vanished, surviving only in combination with other consonants:

χ or h: Initially gave h. Medially (and initially in certain old atonic forms): between vowels > γ > vanished; where h now appears it is due: (1) to some spirant combination (rare), as in Sahóra, and here is only maintained before a stressed vowel, e.g sahóra = saχsōđa, and the development to h < χχ, or to ks < χs is either sporadic or originally dialectal or due to different period of juxtaposition (saxóra appears); (2) to later compositions (PE12/18).