outfit n.

in Old English a common prefix with nouns, adjectives, adverbs, and verbs, "out, outward, outer; forth, away," from out (adv.). The use was even more common in Middle English, and also with the senses "outer, outside, on the outside, from without, external, externally; apart; greatly, extremely; completely, thoroughly, to completion." Other senses of out that extended into the use as a prefix include "beyond the surface or limits; to the utmost degree; to an explicit resolution."

In composition out has either its ordinary adverbial sense, as in outcast, outcome, outlook, etc., or a prepositional force, as in outdoors, or forms transitive verbs denoting a going beyond or surpassing of the object of the verb, in doing the act expressed by the word to which it is prefixed, as in outrun, outshine, outvenom, etc. In the last use especially out may be used with almost any noun or verb. [Century Dictionary]

c. 1400, "to marshal or deploy (troops);" early 15c. as "be fitting or proper, be suitable," from fit (adj.) and perhaps in part from Scandinavian (compare Old Norse fitja "knit"). From 1580s as "be the right shape." Transitive sense of "provide with what is suitable" is from 1590s; that of "make fit or suitable, bring into corresponding form or condition" is from c. 1600. Related: Fitted; fitting. Fitted sheets is attested from 1948.