One way to hold gladly is as glad with a -ly stuck on the end: doing something with gladness inside you. Picture a person who is asked for help and whose face lights up before they answer. That one picture then leans two ways. It can point at the heart behind the answer — yes, and I don't mind at all. Or it can point at the face and the voice at the moment itself — the way a person sounds when good news has just landed.
gladly 可以想成 glad（高興）＋ -ly（……地）：帶著高興去做一件事。畫面是有人開口請你幫忙，你的表情先亮起來，然後才回答。這個畫面可以往兩邊倒。一邊是那份心意——我願意，而且一點都不覺得麻煩。一邊是當下的樣子——好消息剛到，說話的語氣就是高興的。
From the word’s history
From Old English glædlīċe, that is glad + -ly; compare Danish glædelig and Icelandic gleðilegur.
來自古英語 glædlīċe，也就是 glad 加上 -ly；丹麥語 glædelig、冰島語 gleðilegur 是同一條線上的字。所以這個字從一開始就是「帶著高興地」。
Wiktionary etymology supplied in this packet (kaikki:3f6f69a190036ae4:1023470904:17991)
登入就可以看每一支怎麼連回核心畫面。