Old English ahte "owned, possessed," past tense of agan "to own, possess; owe" (see owe). As a past tense of owe, it shared in that word's evolution and meant at times in Middle English "possessed" and "under obligation to pay." It has been detached from owe since 17c., though he aught me ten pounds is recorded as active in East Anglian dialect c. 1825. As an auxiliary verb expressing duty or moral obligation (the main modern use, attested from late 12c.), it represents the past subjunctive.
Ought, Should. Ought is the stronger, expressing especially obligations of duty, with some weaker use in expressing interest or necessity: as, you ought to know, if any one does. Should sometimes expresses duty: as, we should be careful of others' feelings; but generally expresses propriety, expediency, etc.: as, we should dot our i's and cross our t's. [Century Dictionary, 1895]