Duly means as was proper and expected. Duly noted, duly signed, duly arrived.
It has two tones. In formal writing it means properly and in due form: duly authorised, duly appointed, duly served. In speech it often carries a dry note, meaning exactly as everybody predicted — he duly missed the train. Duly noted is the standard reply to a complaint nobody intends to act on. Note that duly is due plus -ly, with the e dropped.
1adverbdulyAs was proper and expected.
“The documents were duly signed and sent back to the bank.”
2adverbexactlyExactly as predicted, with a dry note.
“He said he would never fall off the horse, and he duly fell off within a minute.”
duly is a manner of propriety.
Middle English duely is due plus -ly, and due came from Old French deu, owed, from Latin debere. Debt and duty come from the same owing.
Middle English
duely
English, today
duly
Built from
From Middle English duely, dewly, dulyche, dueliche, duweliche (“rightly, properly”), equivalent to due + -ly.
Etymology from Wiktionary, CC BY-SA