For myself, I take Hobbits to be a diminutive branch of humanity without evolving into Hobbits. In other words, I think they were short and hairy-footed from the beginning. They
seem to have been 'gentle' from early on, at least, as Tolkien notes:
Quote:
'In their unrecorded past they must have been a primitive, indeed 'savage' people*...'
*In the original sense of 'savage'; they were by nature of gentle disposition, neither cruel or vindictive.' JRRT, Of Dwarves And Men
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In any case, if they were always basically 'Hobbits', they did change somewhat in size over time, and diverged in ways, considering the Harfoots and Stoors for example. As a branch of humanity, the Hobbits in
The Lord of the Rings (at least) see themselves as distinct from Men, or the Big Folk, but they are mortal and leave the Circles of the World when they die (based on letter 325 for example).