I was researching a while back and came across an interesting analysis: the tale of Thumbling is the tale of the human spirit traveling through the world. This analysis bounces off a recurring idea that the soul is a tiny being.
In The Annotated Hans Christian Andersen, Maria Tatar suggests that Tom Thumb and Thumbelina were inspired by the Hindu belief of the soul (atman or purusha) as a "thumb-sized being." It seems far-fetched to me that this belief would have migrated through Europe and surfaced in stories like this. I think they were born simply out of the popular interest in what is miniature and fantastical.
She seems to be referring to the ideas set forth in the Upanishads; however, here the soul (atman or purusha) is not described as a thumbling, but as a tiny flame dwelling in the forehead or the heart. It is both infinitely small, the size of a thumb or the thickness of a hair, yet at the same time infinitely huge.
The thumbling soul sometimes appears in Christian imagery (Philosophy and the Self: East and West). In Masolino da Panicle's fresco of the Crucifixion, a tiny man - the soul - emerges from the dying thief's mouth (pictured right).
In a 1520 French stained glass window in the Art Institute of Chicago, the soul of Judas Iscariot is also a tiny man, appearing from his stomach. And in the 1443 "Death of the Virgin" mosaic and other similar artwork, Christ cradles the infant-sized soul of Mary.
Spence suggests in British Fairy Origins that fairies are inspired by images of ghosts - thus fairies are tiny because they resemble the miniature "mannikin soul."
Religion in Essence and Manifestation mentions again the Hindu ideas of the soul. It also describes the Toradja of Celebes [Sulawesi] as imagining a "mannikin" soul, the tonoana. The tonoana is actually one of three souls that each person possesses, and apparently leaves the body to become a werewolf.
James Frazer says in The Golden Bough that in America, the Hurons, Nootkas, and the tribes of the Lower Fraser River all have similar ideas of the soul as a miniature, transparent double of the body. A Wailaki tale from California features a dream doctor who has to hunt down an escaped soul. The soul "resemble[s] a miniature person," and is found sitting by a little fire it's built.
Frazer adds that this is a belief in Malaysia, too. This is a bit of a blanket statement over a group of diverse and complicated beliefs. In Malay tradition, some tribes held that there were actually more than one soul or kind of soul. I did find that Religion in Essence and Manifestation echoes Frazer, citing a chant from Malacca (a state in Malaysia) that refers to the soul as "little" and "filmy" and describes it as a bird. If you go to Wikipedia, it draws from James Hastings' Encyclopedia of Religion and Ethics Part 15, speaking of the soul or "semangat" (essence) being a miniature copy of the body, which flashes from place to place and is compared to a bird. This part of the soul can can leave the body during trances or sleep, and after death, passes into another creature or plant.
In some Chinese stories, the soul is again a tiny double of the body, but this is a relatively rarer and newer idea compared to other Chinese descriptions of the soul.
So the idea of the miniature soul pops up all over the world. The Religion of the Veda basically says all these ideas of the soul as a tiny man probably originated in the Upanishads with the thumb-sized flame. Chronologically speaking, those were recorded around 800-200 B.C., well before any of the other examples listed here.
It still seems like a big step to say that the fairytale characters were descended from a Hindu description of the soul. However, I also remembered that there is a story called "S’homonet com un gri," or the little man as small as a cricket. In this Catalan tale, a couple meets an insect-sized boy, who calls them his parents and helps them around the farm. Thus far, it is a typical type 700 tale; however, he then reveals that he's the spirit of their deceased son, returned temporarily from heaven to aid them.
So maybe Maria Tatar is onto something. However, even though the image of the miniature person could have stemmed from religious art or spiritual imagery, I still think thumbling tales are inspired simply by the appeal of the miniature.
This website is based on my research into folklore.