JRRT purposely made the origin of hobbits a mystery but left
clues, then told us outright in the book, "The Letters of JRR Tolkien".
The hobbits went unnoticed by the peoples who kept written letters and
themselves kept only a vague oral tradition until coming into contact
with the last remnants of the Kingdom of Arnor, the north kingdom. They
have forgotten themselves, mostly. Thus the stories themselves can
hardly do more than
give hints of the origin.
JRRT tells us this in his "Letters" p. 158 footnote which I
paraphrase for brevity:
The Hobbits are meant to be a branch of the human race, not
dwarves or elves. Hence the two kinds can live together as they do in
Bree, calling themselves the Big Folk and the Little Folk. They have no
non-human "powers" but are more in touch with nature such as the soil,
plants, and animals. Abnormally for humans, they are free from ambition
or the greed for wealth. They are small, half human stature and
dwindling with the passing of years. The size is partly to exhibit the
pettiness of plain, unimaginative, parochial man. The other reason is
to show, in creatures of very small physical power, the amazing and
unexpected heroism of ordinary men "at a pinch".
The Hobbit is written purposely in the style of a child's
fairy-tale as a study of ordinary man, neither artistic, noble, nor
heroic but carrying the seeds of these things. The story gradually
shifts into a high setting as the hobbit develops these qualities
during his travels, then purposely shifts style back down with the
hobbit's return home to others who have not been through what he has,
yet with hints of his hidden continuing with the touch of outside and
greatness. For he has the One Ring, by design of the Valar, poised for
the destruction of the rising Shadow in Mirkwood which is Sauron.
Reference: The Letters of JRR Tolkien