In Tolkien's earlier Book of Lost Tales, there were fays, who were minor spirits, as much below the Maiar as the Maiar are below the Valar. Those fays were more or less like Victorian fairies, not like medieval Fairies and Elves. And And when the narrator of The Hobbit mentioned the rumor that one of the Tooks married a fairy wife, Tolkien might have been thinking of an Elf, or thinking of one of those earlier fays. And perhaps some fans consider that rumor to be proof that some sort of "fairies" exist in Middle-earth, even though they are unmentioned in the Silmarillion and The Lord of the Rings.
Going by the species known to exist in Middle-earth, one can speculate that maybe a Took married a Deuedain wild woman, and that wild woman had an ordinary Human amoung her recent ancestors, and that ordinary Human had a Dunedain of Numenorean ancestry amoung their ancestors, and that Numenorean had at least one line of descent from the royal family, and that ment that they were descended from Elves and even from Melian the Maia. And maybe there was still some genetic influence from such remote ancestors in the Tooks.
Or maybe a Took ventured into the Old Forest and met a hypothetical sister of Goldberry, a sister who waswould also be "the River Woman's daughter", whatever the "River Woman" was, and whatever Goldberry's father was.
In the family tree of the Took family, the first named wife is Adamanta Chubb, wife of the Old Took. She seems to have a normal Hobbit name. So possibly the Old Took's mother was the allegedly non Hobbit wife. But the Old Took's granduncle Bandobras "Bullroarer" Took was a very large and fierce Hobbit. So maybe it was the Old Took's great grandfather Thain Isumbras III, father of "Bullroarer" and of the Old Took's grandfather Thain Ferembras II, who married a non Hobbit wife.
Or maybe it was Isumbras I Took, who became the 13th Thain of the Shire, and the first of the Took family, in Third Age 2340, who had an allegedly non Hobbit mother or remoter ancestor. Having a recent non Hobbit ancestor might make Isumbras outstanding, and explain how he was able to acquire the thainship from the Oldbuck family who had it for over 300 years.
[Added 03-17-2024 Or maybe there were two or more Took ancestors who married non Hobbit women of various speciess, which later rhumorsrumors and legends combined into one.]
As to the origins of Hobbits as a group, we can speculate that perhaps there was once a marriage between a Dwarf and a Human, which produced mixed blood children. And maybe one or more of the children married full blood Humans and had 3/4 Human children, the ancestors of the Druedain. And maybe one or more of the other mixed blood children married somone else and was ancestor of the Hobbits.
But in that case, what would the "someone" else be? If it was a Dwarf, that would produce 3/4 Dwarf children, and the Hobbits don't seem like 3/4 Dwarf people. Maybe one or more of the hypothetical Dwarf ancestors might have been a Petty Dwarf. The Petty Dwarves were extra small Dwarves who were expelled for unspecified reasons, perhaps their size, from the Dwarf cities of Belegost and Nogrod in the Blue Mountains during the first age, and moved to Beleriand.
And perhaps some of the Petty Dwarves expelled from the cities in the Blue Mountains went east into Eriador, and met with the ancestors of the Edain moving westward thorugh Eriador, and intermarried with them, producing the ancestors of the Druedain and the Hobbits. If regular Dwarves are only four feet. or a little more, tall, the Petty Dwarves could easily be within the Hobbit height range of two to four feet.
(Of course, if Hobbits were created early enough, the petty Dwarves might have been mixed offspring of regular Dwarves and Hobbits!)
Considering the difference between Dwarves and Hobbits, and between most Men and Hobbits, we would want some other species besides Dwarves and Men in the Hobbit ancestry. Elves seem to be unlikely because of the differences between Elves and Hobbits. Trolls seem unlikely because of the differences betwen them and Hobbits. And what does that leave?
Orcs. I note that the Tower of Cirith Ungol, with a garrison of only a few hundred orcs, had some Orc clothing and equipment that fit Sam and Frodo fairly well, and that when they later encountered Orcs while wearing Orc clothing, those Orcs assumed they were other Orcs. Thus some breeds or races of Orcs seem to have been as short as Hobbits.>
Did a Human woman escape from Orc capitivity with a half Orc child who became an ancestor of the Hobbits? Or did Humans, or Dwarves, or Elves, wipe out a band of Orcs and find a baby Orc among them, and someone raised the baby Orc, and it became a relatively good person and an ancestor of Hobbits?
Or may be all Hobbits were partially descended from marriages between Humans and members of some species unknown to fans and not on Treebeard's list Like the three species mentioned in The HobbitThe Hobbit, but not in The Silmarillion orThe Silmarillion or in The Lord of the Rings The Lord of the Rings: Fairies, Ogres, and Giants.
Or maybe Morgoth or Sauron experimented with creating a race they considered inferior during the First Age. Maybe they planned to breed vast numbers of them and then set them free to mingle with and intermarry with Elves and Men. If they made certain that the genes of that species were all dominent, any mixed blood offspring would resemble that species and not any Elves or Men they intermarried with.
So they would design that species to be small and physicially weak, unable to fight effectively against armies of Orcs, and evil Men, and Trolls, and Balrogs, and Dragons. And they hoped that if they intermarried a lot with Elves and Men they would produce weak offspring to weaken those species.
And maybe Sauron suggested to Morgoth that maybe they should make that species kind and gentle. And maybe the shocked Morgoth asked why he would think such a disgusting thought. And Sauron explained that way they would get along better with Elves and Men and be more likely to intermarry with them and produce small, weak offspring. And maybe Morgoth agreed.
And maybe something prevented the breeding of great numbers of that sabotage species, but some were bred and got free someone from UttumnoUtumno or Angband, and became the ancestors of Hobbits, or intermarried with other species to be part ancestors of Hobbits.
If mortal Men first awoke with the first rising of th ethe Sun, about 590 years before the end of the First Age, and the Second Age lasted 3,441 years, and Hobbits were first recorded in year 1050 of the Third Age, that gives only about 5,081 years for Hobbits to become separate from typical Humans.
That seems far too short a time for natural evolution to produce such a vast change in a group with such long generations.
So either:
That seems far too short a time for natural evolution to produce such a vast change in a group with such long generations.
So either:
One) Either Eru Created the first Hobbits (and Druedain) the way they always were, and they awoke among the other Men with the first rising of the Sun.
Three) someoneSomeone found some early humans after they had awakened with the rising of the Sun, and took them, and experimented on them, and produced Hobbits.
Or
Four) sometimeSometime after the first rising of the Sun, some early Humans intermarried with members of one or more other species and produced the first Hobbits.