I've noticed a tendency for some thumbling tales to mention the sun - often in roles that overlap. In two stories, the sun is a negative force. Also in two stories, it is somehow the reason why the thumbling is so small, and in a third, it's the reason why mice are so small.
On the surface, there's an odd similarity between these tales from North America, Burma, and England, respectively. Upon a closer look, however, these stories all came from very different lines of reasoning.

In the Anishinaabe narrative of "Little Brother Snares the Sun," the Sun offends a very small child by shrinking his favorite coat. In retaliation, the boy captures the Sun in a magical net made from his sister's hair. A mouse frees the sun, but in the process shrinks down to its current tiny size.

In the Burmese tale "How Master Thumb Defeated the Sun," the Sun curses a pregnant woman so that her child is only the size of a finger. This child later goes to fight the Sun as a result. (Maung Htin Aung, who retold this story in English, theorized that this was a descendant of a solar myth.)

So the Sun has the power to shrink things with its heat - something easily observed in the real world, but usually with the excessively high heat of a clothes dryer, not simple sunlight.
Typically, the Sun is most familiar as a symbol of warmth and life, which causes plants to grow, but in these stories, it is a negative figure associated with heatstroke and drought.

As Maung Htin Aung explains in the notes to Master Thumb,

Here, rain is an ally and the Sun is the enemy. Maung Htin Aung contrasts this with a version from Lower Burma, where Master Thumb is angry at the Sun but his followers are just kind of hanging out. In Lower Burma, the summer heat is not as intense.

As for Little Brother, Richard L. Dieterle points out that Little Brother's coat is made from a snowbird's skin. The character is thus associated with snow, clouds and winter, the antithesis of the sun and its heat.
However, here the Sun is still necessary. It's not as much of a character as the one in Master Thumb's version, just a force of nature. Trapping it leaves the world in darkness, and all will perish without it. Unlike the story of Master Thumb, here the animals (and thus the world itself), instead of helping the sun-catcher, endeavor to save the sun.

So those two tales have similarities on the surface, but their internal logic goes a little differently. However, it's interesting that Master Thumb's small size is caused by the Sun. In the English Tom Thumb’s Folio, or, A new penny play-thing for little giants (1791), a solar eclipse "stinted [Tom's] growth."

This is stated very casually, as if it's something to be expected from a solar eclipse. Is it because eclipses are times when crazy things happen and nature is turned on its head, or is it that the absence of the sun means that things (from crops to children) cannot grow and develop normally?
The sun does actually promote vitamin D, which improves bone growth, so there is a physical, scientific reason. This is also a story written by an English writer. England is not sunny. Here, unlike Upper Burma, the Sun is a more positive figure, and its absence is a bad thing.
There are superstitions, particularly in India and Latin America, that an eclipse can be harmful to pregnant mothers, causing children to be born with deformities like cleft lips or birthmarks. In Medieval Europe, the thought was that children conceived during an eclipse would have demons.

That's just one retelling of Tom Thumb, but even in other tales, he may, like Little Brother, be a creature averse to the sun.
The fairies with whom he was sometimes associated (as in Robin Goodfellow and Nymphidia) were nocturnal beings often depicted living underground.
Like quite a few other thumblings, Tom rides a mouse, which also lives underground in the dark. Many thumblings are associated with mice - harnessing them to chariots, being compared to them for a size reference, or actually being mice, like "Hasan the Heroic Mouse-Child."
In Norse myth, dwarves are subterranean creatures of shadow, and sunlight will turn them to stone. Dwarves are a step removed from thumblings, but of the same folkloric family.

Despite the different lines of logic, the result is still that a few thumbling tales have a similar connection to the sun. Due to the great distance between them and the obviously different origins, it seems to be mere coincidence. Still, the similarities are intriguing.

​Tom Thumb is a star in the constellation of the Big Dipper. Specifically, Alcor, a barely-visible star right in the middle of the dipper’s handle, piggybacking on a star called Mizar. 

According to Le Petit Poucet et la Grande Ourse, or “Tom Thumb and the Great Bear,” by Gaston Paris, there's a little-heard-of tradition in Wallonia regarding this constellation. Here, its name is “Chaûr-Pôcè."

The idea is that the four stars on the right are the wheels of a cart, and the three in line on the left are horses. Sitting on the horse in the middle is tiny Alcor. This is the driver, Pôcè – or Poucet, i.e. Tom Thumb. (This is sourced from Grandgagnage’s etymological dictionary.) Apparently the tradition is that Poucet is hanging beneath the belly of the second horse, trying to reattach the harness.

I’ve seen other sources refer to this constellation as a wain or wagon, and there was an Arabic tradition of calling Alcor and neighboring star Mizar the horse and rider, but this is the only time I’ve heard Tom Thumb in astronomy.

Paris is basing all this in theories that all myths are connected and furthermore they all have astronomical ties. He links it further, by a few leaps, to the myth of baby Hermes stealing the oxen. This seems a bit much. (Like Tom Thumb being Tam Lin.)

​However, many variants of the Thumbling folktale do include him riding horses and donkeys (usually perched in an ear) or driving a plow pulled by horses or oxen. This, coupled with how hard it is to see Alcor, makes the name seem quite appropriate.