In a way that is correct, just, or legally proper according to rules or justice.
From Old English 'riht' (straight, correct) plus 'full' and the adverbial suffix '-ly.' The word evolved from describing physical straightness to moral and legal correctness, then to the adverbial form meaning 'in a rightful manner.'
The word 'rightfully' shows how language evolved from describing physical properties (straight) to abstract concepts (correct/just)—a pattern you see throughout English where concrete meanings become metaphorical over time.
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