Lean, spare, lank, lanky, gaunt, rawboned, scrawny, skinny mean thin because of an absence of excess flesh See ‘meaning & use’ for definitions, usage, and quotation evidence. Lean stresses lack of fat and of curving contours.
See examples of skinny used in a sentence. There are 14 meanings listed in oed's entry for the word skinny, three of which are labelled obsolete The meaning associated with lack of fat or muscle possibly derives from the phrase skin and bones
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