Evolution made 'em.
Really. There's linguistic evidence in the texts that at some point they shared land with the ancestors of the Rohirrim - this could indeed have been a common ancestor from which descended both the contemporary Hobbits and Rohirrim. I've got something aeons old posted somewhere on here about that when I uncovered it, but I shall have to find it when I get a chance.
It's likely that this was Tolkien's desired intention as his work was as much constructed as a place in which to explore his created languages and their evolution as it was about many other things. To demonstrate common ancestry via linguistic roots is extremely apt for Tolkien. Note he also adds in the existence of faded legends of Hobbits amongst the Rohirrim, which adds extra texture to this sense of history.
How about the other evidence that the Ents did not know of Hobbits, Ents who were taught by the Elves? Here are two long lived races who know nothing of Hobbits so it is clear they originated elsewhere and at a later stage.
And who wants to have Tolkien write a Noddy Guide as to where Hobbits came from? It's far more fun to find out for yourself on a chance discovery like a real life etymologist or archaeologist striking gold in the stacks at the British Library or somesuch
Plus it only adds to their folky mystique, like the boggarts, the hobgoblins and the brownies that live in our houses...