[Son of Númenor]

This should answer your question:

It is plain indeed that in spite of later estrangement Hobbits are relatives of ours: far nearer to us than Elves, or even Dwarves. Of old they spoke the languages of Men, after their own fashion, and liked and disliked much the same things as Men did. But what exactly our relationship is can no longer be discovered. The beginning of Hobbits lies far back in the Elder Days that are now lost and forgotten. Only the Elves still preserve any records of that vanished time, and their traditions are concerned almost entirely with their own history, in which Men appear seldom and Hobbits are not mentioned at all. Yet it is clear that Hobbits had, in fact, lived quietly in Middle-earth for many long years before other folk became even aware of them (The Lord of the Rings, "Prologue", 2).

Hobbits are descended from Men. How they evolved into the little, reclusive people that they are is never made clear.

Edit: I cross-posted with you, Carnimírië. Nice find in the Letters.