Very thin and skinny, like a twig, or having lots of twigs and branches.
From 'twig' (a small thin branch) plus '-y' (having the quality of); straightforward descriptive word comparing something thin to a thin branch.
The 1960s model Twiggy got her nickname because she was extremely thin by the standards of the time—her look started a beauty revolution where 'skinny' became fashionable instead of curvy, completely changing fashion forever.
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