In a manner that is dull, bleak, or depressing.
From 'dreary' (Old English 'dreore') + '-ly'. This is the standard adverbial form of the common adjective 'dreary', following regular English word formation patterns.
While 'dreary' became common in Middle English, 'drearly' as an adverb is interesting because some people prefer just using 'dreary' as an adjective even when an adverb is needed—showing how language shortcuts develop.
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