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"looking well," 1560s, from earlier sense of "fitting" (early 13c.), from present participle of become. Related: Becomingly; becomingness.
Old English becuman "happen, come about," also "meet with, arrive," from Proto-Germanic *bikweman "become" (cf. Dutch bekomen, Old High German biqueman "obtain," German bekommen, Gothic biquiman). A compound of be- and come; it drove out Old English weorðan. Meaning "to look well" is early 14c., from earlier sense of "to agree with, be fitting" (early 13c.).