Entries linking to outweigh
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]
The original sense was of motion, which led to that of lifting, then to that of "measure the weight of." The older sense of "lift, carry" survives in the nautical phrase weigh anchor. Figurative sense of "to consider, ponder" (in reference to words, etc.) is recorded from mid-14c. To weigh in in the literal sense is from 1868, originally of jockeys; figurative meaning "bring one's influence to bear" is from 1909.
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these considerations outweigh our wishes