assess (v.)

early 15c., "to fix the amount (of a tax, fine, etc.)," from Anglo-French assesser, from Medieval Latin assessare "fix a tax upon," originally frequentative of Latin assessus "a sitting by," past participle of assidere/adsidere "to sit beside" (and thus to assist in the office of a judge), "sit with in counsel or office," from ad "to" (see ad-) + sedere "to sit" (from PIE root *sed- (1) "to sit").

One job of the judge's assistant was to fix the amount of a fine or tax. The meaning "to estimate the value of property for the purpose of taxing it" is from 1809; the transferred sense of "to judge the value of" (a person, idea, etc.) is from 1934. Related: Assessed; assessing.