Admiringly is from admiring plus -ly. The suffix -ly recasts admiring as an adverb: the lexical idea remains recognizable, but the word now describes manner, degree, or circumstance rather than naming the quality by itself. In use as an adverb, admiringly denotes in a way that shows respect, approval, or pleasure. Typical contexts include “She looked at the painting admiringly for a long time”. The meaning stays close to the form: it applies the etymological material to in a way that shows respect, approval, or pleasure, keeping the visible parts legible in ordinary use.