In a manner worthy of scorn or deserving contempt; in a despicable way.
From contemnible plus -ly (adverbial suffix). This creates an adverb by adding the standard English adverb-forming suffix to the adjective form.
The proliferation of -ly adverbs from the same root (contemn → contemnible → contemnibly) shows how productive English morphology is—you can keep stacking suffixes to modify meaning and word class, though not all combinations remain in active use.
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