Etymology
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duly (adv.)

"rightly, properly; adequately, sufficiently; in accordance with duty or moral obligation," late 14c., duweliche, from dewe "due" (see due) + -liche (see -ly (2)).

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Definitions of duly

duly (adv.)
in accordance with what is appropriate or suitable for the circumstances;
I met the junior senator from Illinois and I was duly impressed
Synonyms: appropriately / suitably / fittingly / befittingly / fitly / properly
From wordnet.princeton.edu