In a joyful, merry, or delighted way; with obvious happiness and excitement.
From glee (Old English gleo meaning 'entertainment' or 'music') + -ful (full of) + -ly (adverb marker). The original meaning was related to music and entertainment.
The word 'glee' started meaning 'music' in Old English, which is why it specifically means a kind of joy that wants to express itself—it's etymologically connected to singing.
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