A root in the Qenya Lexicon of the 1910s glossed “sigh, say alas”, with derivatives like ᴱQ. siqi- “sigh” and ᴱQ. siqilisse “lamentation; weeping willow” (QL/84). It also had derivatives in the contemporaneous Gnomish Lexicon such as G. sibra- “weep, whimper” and G. sigweth “lamentation, weeping” (GL/67). I think it is worth positing an Neo-Root ᴺ√SIKW “sigh” to salvage some of these early words.
Quenya
siqu-
sigh
siqu- ("q")vb. "sigh" (cited in form "siqi"), pa.t. síque (QL:84)