Where do hobbits come from?

[The Saucepan Man]

I'm not at all sure that there was sufficient time while Gollum was under the mountain for 6'+ men to evolve into 3-4' hobbits. And anyway, the theory of evolution doesn't really fit in with Tolkien's presentation of ME and its history.

As for Gollum not recognising Bilbo's stock, well his brain was addled from too many Goblin curries.

I would hold with those who speculate that hobbits were a smaller variety of man who awoke at the same time and (as hobbits are wont to do) kept themselves to themselves.