Hobbits were a sub-group of humans. There were three statements to this effect. The first, from the Prologue, is probably less definite because it was intended to be the editor speaking.
It is plain indeed that in spite of later estrangement Hobbits are relatives of ours: far nearer to us than Elves, or even than 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.
[The Fellowship of the Ring, 11 (Prologue)]
The Hobbits are, of course, really meant to be a branch of the specifically *human* race (not Elves or Dwarves) - hence the two kinds can dwell together (as at Bree), and are called just the Big Folk and Little Folk. They are entirely without non-human powers, but are represented as being more in touch with 'nature' (the soil and other living things, plants and animals), and abnormally, for humans, free from ambition or greed of wealth.
[The Letters of J.R.R. Tolkien, 158 (footnote) (#131)]
The Firstborn:
Title of the Elves. Translate. ('Firstborn', since the Elves appeared in the world before all other 'speaking peoples', not only Men, but also Dwarves, of independent origin. Hobbits are of course meant to be a special variety of the human race).
[A Tolkien Compass, entry for "The Firstborn"]
My theory - Hobbits are party elven:
I think, that the hobbits partly derived from the people. But only partly. Their roots, as I think, are in the Avari.
Because, where did these Avari disappear to?
As my theory says, the Avari came along with the Western Easterlings (of Bor's kin), and they mixed up to the hobbitfolk.
Why do I think so?
First, because the Avari did not disappear. Some of them must've gone a little westerner, towards Mirkwood, which is not so far from Cuivienen. All this happened through the Age of Melkor's unchaining, and through the 1st Age.
Second, their "inner strength," as Gandalf calls it. In some places he mentions, that the hobbits are hardier than people.
For example: after Frodo was stabbed in his shoulder at Amon-Sûl withstood 17 days.
After the Chief Nazgúl gave Merry the black breath in Pelennor, Aragorn says to the hospital man, that the hobbits are hardy, despite their small height.
From what can this hardiness come?
Here we can see a sign of Elfish past, for the Elves are hardier than people, and the hobbits have inherited it.
Another clue is the love for water in the hobbits, or, I should say, in the Stoors, a branch of them.
As Gandalf says:
Long after [After the year 3 T. A., in which Isildur died M.B.], but still very long ago [About the year 2469 T.A. {See The Lord of the Rings, Appendix B} M.B.], there lived by the banks of the Great River on the edge of Wilderland a clever-handed and quiet-footed little people. I guess they were of hobbit-kind; akin to the fathers of the fathers of the Stoors, for they loved the River, and often swam in it, or made little boats of reeds.
[The Shadow of the Past, The Lord of the Rings]
It's commonly known that the Elves loved water; and this was also inherited form them by the hobbits.
Those were the Nandor; and they became a people apart, unlike their kin, save that they loved water, and dwelt most beside falls and running streams.
[Quenta Silmarillion, The Silmarillion]
The Nandor derived from the Teleri, of whom part remained near Cuivienen became Avari. From this we can deduce that the Avari liked water and part of the hobbits has inherited it, too.
Another explanation for my hypothesis is the place of the first hobbit settlement. You can see that in that place there lived Avari and Western Easterlings, which could've mixed up, as explained above.
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