Gladly means willingly and with pleasure. I would gladly help, gladly accepted, gladly given.
It answers a request rather than describing a mood — saying you would gladly do something is an offer. It is slightly formal and warm. Note that not gladly suffer fools comes from a biblical phrase and means having no patience with them.
1adverbgladlyWillingly and with pleasure.
“I'll gladly help you move house this weekend.”
gladly is a manner.
Old English gladlice is glad plus the -lice ending that makes adverbs. Glad first meant bright or shining.
Old English
glædlīċe — gladly
Middle English
gladly
English, today
gladly
From Middle English gladly, gladliche, from Old English glædlīċe (“gladly”); equivalent to glad + -ly. Compare Danish glædelig (“joyful”), Icelandic gleðilegur (“delightful”). More at glad, -ly.
Etymology from Wiktionary, CC BY-SA