Three close cousins: 唯一 = the only one (adjective), 唯有 = only (literary adverb, fronts a clause), 唯独 = only / except (singles one item out). 惟 is a near-synonym variant historically interchangeable in most of these compounds.
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唯 has a second classical reading 唯 meaning 'yes' — the deferential 'aye, sir' a subordinate gives a superior. You will not hear it in modern speech; it survives only in literary quotations and in the etymology of the mouth radical here.
Left mouth radical — marks 唯 as a speech-act. Originally an emphatic assent particle in Classical Chinese (read wěi, 'aye, sir'). From this singular spoken assent the meaning generalised to 'only, solely' — the modern adverb.
Right component supplies the sound (zhuī → wéi) — an irregular but established phonetic match seen across the family in 维 (tie) and 谁 (who). Purely phonetic here; the 'short-tailed bird' meaning of 隹 carries no semantic weight in 唯.
