Is it farther or further?
mid-13c., "unblemished, refined, pure; of superior quality," from Old French fin "perfected, of highest quality" (12c.), from Latin finis "end, limit" (see finish); hence "acme, peak, height," as in finis boni "the highest good."
In French, the main meaning remains "delicate, intricately skillful;" in English since mid-15c. fine is also a general expression of admiration or approval, the equivalent of French beau (cf. fine arts, 1767, translating French beaux-arts). Finer; finest. Fine print is from 1861 as "type small and close-set;" by 1934 as "qualifications and limitations of a deal."
c.1200, "termination," from Old French fin "end, limit, boundary; death; fee, payment, finance, money" (10c.), from Medieval Latin finis "a payment in settlement, fine or tax," from Latin finis "end" (see finish).
Modern meaning is via sense of "sum of money paid for exemption from punishment or to compensate for injury" (mid-14c., from the same sense in Anglo-French, late 13c.) and from phrases such as to make fine "make one's peace, settle a matter" (c.1300). Meaning "sum of money imposed as penalty for some offense" is first recorded 1520s.
late 13c., "pay as a ransom or penalty," from fine (n.). Inverted meaning "to punish by a fine" is from 1550s. Related: Fined; fining.