Thanks to /u/Artillect for the summons and the links provided.
Several books could be written on the subjects raised by this post. Besides the answers in the links, we can consider a few things. First, I'm not sure what is meant by the term "ancient mythology." Almost everything that is known about Northern European elves and their kin is from pre-modern/pre-industrial folklore collections of the nineteenth and twentieth centuries. In addition, there are some examples from medieval literature that allude to beliefs that are apparently related and are precursors of what was documented several centuries later by the first European folklorists.
Northern European pre-modern folklore exhibited a remarkable array of traditions that hung together with a great deal of common ground. Whether referred to as fairies, sí (Gaelic, pronounced "she"), elves, various Scandinavian terms that can be translated as "hidden folk," various Scandinavian terms related to the word "troll" (except the term was also be used in some places for other non-fairy-like entities) and other words. While the traditions associated with these various terms are different, they share common ground and are often described in similar legends and folktales. At the core of these traditions is the idea that these supernatural entities live in communities and often families that directly reflect the human condition. For the most part, elsewhere, similar supernatural beings appear in singular form or in multiples that nevertheless behave in a unified, singular way. We can, consequently, regard the Northern European supernatural beings lumped together with these terms as homogeneous in many ways. That is the baseline that inspired and fascinated authors of the nineteenth and twentieth centuries.
‘Songs of the Pixies’ by Samuel Taylor Coleridge appeared in 1796; it is an early example of literary adaptation of folklore about these entities. More importantly, Anna Eliza Kempe Bray (ca. 1790–1883) celebrated south west British pixies in letters to Romantic-era poet Robert Southey, printed in 1836. Two years later, she consolidated her writing in "Traditions, Legends, Superstitions, and Sketches of Devonshire on the Borders of the Tamar and the Tavy," and pixies began a journey as the shared property of the English-speaking world. In 1854, Bray furthered the advance of pixies into popular culture with her children’s book, "A Peep at the Pixies, or Legends of the West."
Because Bray was extremely popular and she worked with a variety of fairy from south west Britain that was usually described in small form, the popular imagination of the literate English-speaking world (which was detached from pre-modern folklore) began to think of fairies/elves as small.
Coincidentally, the idea that they had wings emerged, even though the pre-modern folk tradition included nothing of the kind: the history of wings being attached to fairies is another issue and it is very complex, but briefly: it began occurring probably as an analogy adopted from classical Roman depictions of cupid-like entities who were often depicted with wings; this motif began to be employed in part as a consequence of Renaissance-era exploration of classical motifs. The adoption of wings was slow, until it accelerated in the nineteenth century, in part because Bray began depicting her pixies as small, cute, and flying about flowers, making them a target for illustrators who gave them insect wings. But that is a digression that does not help us with OP's question.
After Bray, other authors began looking to the body of folklore associated with the array of related supernatural beings as inspiration for their writings. Again, volumes could be written on this, but there is no question that when Tolkien dipped into this well, he set a standard that had a profound influence on subsequent literature in the genre.
Tolkien by-passed the small pixies of Bray, entities that dominated much of subsequent literary adaptations of the nineteenth and early twentieth century. Instead, Tolkien returned to the more stately, human-sized examples. Traditions from Wales and parts of Scandinavia can be regarded as similar to the motif as expressed by Tolkien. There are many who have delved into this more thoroughly than I have, but it is clear that by working with the Northern European body of tradition, drawing on examples other than the smallish pixy, Tolkien re-calibrated the way the English-speaking world thought of elves.
With the previously linked answers and some of this, I hope these are some thoughts here that are of use. Let me know if you have further questions.