With great power, strength, or effort; in a mighty way.
From 'mighty' (Old English 'mihtig' from 'miht' meaning power or strength) plus '-ly' to make it an adverb. The root relates to 'might' as in power or possibility.
The word 'might' in 'mightily' is different from the helping verb 'might'—one means power, the other expresses possibility, but they come from the same ancient root, showing how a single old word fractured into multiple modern meanings.
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