Picture something worked down until the pieces are almost too small to see: onion under a knife, a wheel inside a watch, a leaf cut into wood. Finely describes that working-down. What changes from sense to sense is where the smallness lands — in the pieces themselves, in how exact the work is, or in how much skill you can see in the result.
From the word’s history
Wiktionary traces finely to Middle English finely, equivalent to fine + -ly. The English adjective fine already carries two things at once — small or thin, and good — and the adverb inherits both, which is why this one word covers chopping and carving.
資料裡記著 finely 來自中古英語 finely，也就是 fine 加上 -ly。英文的 fine 本來就同時帶著兩層意思：一層是細、薄，一層是好、精緻。finely 把兩層都接了下來，所以同一個字才會既能講切洋蔥，也能講雕花。
evidence packet: Wiktionary (kaikki) etymology_text for finely — "From Middle English finely, fynely, fynly, fineliche... equivalent to fine + -ly."
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