Let me answer your last question first: a sweet tooth is a synecdoche, a figure of speech in which "a part is used for the whole or the whole for a part" (Webster's Dictionary, New York 1994, or online).
I can't provide a sound derivation for that idiom, as the sources available to me (easily, I'm sorry I can't comb through the 284,000 Google results) with etymological information about it are pointing to the 14th century as to its origin, provide the meaning we're referring to today (see, e.g., OED), but don't explain if this really was the first and original meaning.
(As to dating, let me tell you that finding a book from the 17th century containing the term in question doesn't mean the term originated in that period while other sources claim an earlier date. What you find on the first three pages of an ad-hoc internet search is never the big picture.)
But let us take a closer look at that source you found, the Nouvelle Facile Methode Pour Apprende l'Anglois, from 1698. The portion of the text containing our sweet tooth quote reads as follows:
The great Mutton is commonly course [coarse], and is not for a sweet Tooth. – But the small Mutton (or rather the middle size) such as feeds in dry Pastures, is very palatable.
Sweet doesn't necessarily mean tasting like sugar but can also mean fresh, pleasing, delicate, agreeable, dear, or easily managed. Now that we have the pair of opposites: not for the sweet tooth/palatable referring to mutton it seems highly improbable that sweet should mean sugarlike in this context, but, as palatable suggests, rather something like pleasing or delicate.
Now mind the left column providing a French translation of the English text:
Le gros Mouton est generalement grossier, & ne se mange guere parmi les honnêtes gens. – Mais le petit Mouton, qui pait dans les Lieux
secs, a un Gout fort agreable. [The big mutton is coarse in general
and is hardly appreciated among noble people. But the small mutton,
feeding on dry pastures, has a very pleasing taste.]
This gives us a hint what people having a sweet tooth might have meant originally: People who are very delicate and paticular about what they eat, implying people from the upper classes who could afford being delicate.