E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
means in tide, in season, in time. We retain the word in even-tide, spring-tide, and so on. Tusser has the phrase, If the weather be fair and tidy, meaning seasonable. Things done punctually and in their proper season are sure to be done orderly, and what is orderly done is neat and well arranged. Hence we get the notion of methodical, neat, well-arranged, associated with tidy. (Danish, tidig, seasonable, favourable.)
How are you getting on? Oh! pretty tidilyfavourably (See above.)
A tidy fortune. A nice little bit of money. Tidy means neat, and neat means comfortable.