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mid-15c., from Middle French estimer (14c.), from Latin aestimare "to value, appraise," perhaps ultimately from *ais-temos "one who cuts copper," i.e. mints money (but de Vaan finds this "not very credible"). At first used as we would now use estimate; sense of "value, respect" is 1530s. Related: Esteemed; esteeming.
(also steem, extyme), mid-14c., "account, worth," from French estime, from estimer (see esteem (v.)). Meaning "high regard" is from 1610s.