In a greasy, oily, or slippery manner; with a greasy quality or characteristic.
From 'greasy' + '-ly' (adverb-forming suffix); this creates an adverb describing how something is done in a greasy way, or describing a quality that is manifested greasily.
The adverb 'greasily' can mean both 'in a physically oily way' (the food cooked greasily in the pan) and figuratively 'in an oily, ingratiating way' (he spoke greasily, trying to manipulate her), showing how physical properties become metaphors for character.
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