"suit ill, be unfitting," 1520s, from mis- (1) "badly, wrongly" + become.
Entries linking to misbecome
mis- 1
prefix of Germanic origin affixed to nouns and verbs and meaning "bad, wrong," from Old English mis-, from Proto-Germanic *missa- "divergent, astray" (source also of Old Frisian and Old Saxon mis-, Middle Dutch misse-, Old High German missa-, German miß-, Old Norse mis-, Gothic missa-), perhaps literally "in a changed manner," and with a root sense of "difference, change" (compare Gothic misso "mutually"), and thus possibly from PIE *mit-to-, from root *mei- (1) "to change."
Productive as word-forming element in Old English (as in mislæran "to give bad advice, teach amiss"). In 14c.-16c. in a few verbs its sense began to be felt as "unfavorably," and it came to be used as an intensive prefix with words already expressing negative feeling (as in misdoubt). Practically a separate word in Old and early Middle English (and often written as such). Old English also had an adjective (mislic "diverse, unlike, various") and an adverb (mislice "in various directions, wrongly, astray") derived from it, corresponding to German misslich (adj.). It has become confused with mis- (2).
become v.
Middle English bicomen, from Old English becuman "happen, come about, befall," also "meet with, fall in with; arrive, approach, enter," from Proto-Germanic *bikweman (source also of Dutch bekomen, Old High German biqueman "obtain," German bekommen, Gothic biquiman). A compound of the sources of be- and come (v.).
It drove out Old English weorðan "to befall." The older sense is preserved in what has become of it? The meaning "change from one state of existence to another" is from 12c. The meaning "to look well, suit or be suitable to" is by early 14c., from the earlier sense of "to agree with, be fitting or proper" (early 13c.).