The OED netry for tariff, noun, gives the etymology as from the Italian originally and this agrees with its first known usage which also relates to the Italian spelling.
Etymology
Etymology: < Italian tariffa ‘arithmetike or casting of accounts’ (Florio), ‘a book of rates for duties’ (Baretti), = Spanish tarifa, Portuguese tarifa, < Arabic taʿrīf notification, explanation, definition, article, < ʿarafa in 1st conj. to notify, make known. So French tarif.
The word came into general use as a technical term (sense 2), and this character it long retained in English use, being hardly found, except as applied to the Customs ‘tariff’; its more general application (sense 3), found earlier on the Continent and in U.S., has become more common in Great Britain only since c1890.
Usage
†1. An arithmetical table or statement; a table of multiplication, a ready reckoner, or the like.
1591 W. Garrard & R. Hitchcock Arte of Warre 224 So that helping your memorie with certain Tablei or Tariffas made of purpose to know the numbers of the souldiers that are to enter into ranke.