Assess
late Middle English: from Old French assesser, based on Latin assidere ‘sit by’ (in medieval Latin ‘levy tax’), from ad- ‘to, at’ + sedere ‘sit’. Compare with assize.
wiktionary
From Middle English assessen, from Old French assesser, from Medieval Latin assessare, originally the frequentative of Latin assessus, past participle of assidēre, from ad(“to, towards, at”) + sedeō(“sit; settle down”). Cognate with Spanish asentar(“to settle”).
etymonline
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. Meaning "to estimate the value of property for the purpose of taxing it" is from 1809; transferred sense of "to judge the value of" (a person, idea, etc.) is from 1934. Related: Assessed; assessing.