In a way that shows warmth, enthusiasm, or bright approval; with genuine positive emotion.
From 'glowing' (the present participle of 'glow,' from Old English glōwan) plus the adverbial suffix '-ly.' The metaphorical sense of 'glowing with pride' or 'glowing praise' developed in Middle English.
When you describe something 'glowingly,' you're actually using light as a metaphor for emotional warmth—the same reason we say people 'light up' when happy or 'shine' when doing well.
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