One way to picture mildly: someone has turned the dial down a notch. Mild already means not strong and not sharp, and -ly turns that into a way of doing things. The dial can be turned down on an amount, so heat or feeling is there but small. It can also be turned down on a manner, so a voice stays flat where it could have risen. Either way the thing is still present; only the force is low.
From the word’s history
The evidence packet's Wiktionary entry gives mildly as mild + -ly, with mild going back through Middle and Old English (milde). The old sense of mild is not harsh, not severe, which is exactly the low-force picture the modern adverb still carries.
證據包中的 Wiktionary 記載 mildly 就是 mild 加上副詞字尾 -ly，而 mild 可上溯到古英語 milde。mild 早期的意思是「不嚴厲、不刺激」，這正好就是今天 mildly 仍然帶著的那個「力道很小」的畫面。
Wiktionary entry for mildly, kaikki extract supplied in this evidence packet (source_ref kaikki:3f6f69a190036ae4:891677446:6157)
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