There is not, to be the best of my knowledge, any universally-agreed upon reason where certain popular mythological concepts "originated" from. The current conception of elves and dwarfs in contemporary popular culture owes much to The Lord of the Rings and subsequent works influenced by Tolkien's fiction; Tolkien in turn drew on the folklore and mythology of the British Isles and Scandinavia, in particular the svartálfar or dökkálfar ("black elves" or "dark elves") and ljósálfar or hvítálfar ("light elves" or "white elves") - and this is itself rather complicated, and resists easy generalizations; many of the attributes that Tolkien and subsequent authors used for elves and dwarfs art taken from these concepts, but it's not a direct translation. u/itsallfolklore and I talk a bit about this in this thread and u/itsallfolklore tackles some questions about the "origin" of these various supernatural "classes" of entity here.
Beyond literary interpretations and popularization, there was a popular conception (especially in the late 19th/early 20th century) called Euhemerism: the idea that mythology contained a kernel of historical truth or was based on an inspirational incident/phenomena. This approach is largely discredited - there just isn't an accurate historical record to support some of the arguments for what historical incident or phenomena "inspired" certain myths. For dwarfs, for example, we can honestly say that different populations in history had differences in height (due to diet, genetics, etc.), and we know that there are medical conditions that cause short stature in humans. But it's a leap from there to say that the idea of dwarfs (or svartalfar, etc.) were caused by prehistoric contact with a shorter group of peoples, or from local experiences with a family with growth hormone disorders or anything like that. The myths just predate any historical record like that, so you're left in the realm of supposition. A really good book on Euhemerism and some of the impact it had on society and literature is Carole G. Silver's Strange and Secret Peoples: Fairies and Victorian Consciousness.
As always, the esteemed /u/AncientHistory does excellent work here. The question presented by OP can be interpreted as wondering about the origin of the literary references or about the origin of the folk belief. The literary references are a tangle, but they are in some ways easier to unpack than the origin of folk belief. Although one can - as /u/AncientHistory suggests - go to the Icelandic Prose Edda of Snorri Sturluson for the terms that are translated dark and light elves as an inspiration for Tolkien, much of his idea of the courtly elfin realm can be traced to published folklore about the Tylwyth Teg the Welsh counterpart of the fairies throughout Northern Europe. But all of this is along the lines of attempting to untangle the sources of inspiration for Tolkien, a well-read scholar with this fingertips touching diverse sources.
If on the other hand, one is to ask about the origin of belief in the supernatural beings of Northern Europe, the task becomes much more difficult. It is, simply, not possible to say anything definitively about the origin of the fairies/elves/piskies/huldrefolk/etc., (there are many terms for these entities depending on the place). They are widespread in Northern Europe, allowing for diffusion of stories because of the shared belief system, but it is not likely that the beliefs themselves diffused since that is a taller order: it is difficult to cause a culture to change its folk belief colors, especially in a pre-literate society, so we can assume that this shared inheritance is very old.
Since all cultures have supernatural beings of some sort, trying to come to grips with the origin of these beliefs can do little more than to take us down a rabbit hole from which we are not likely to emerge with our wits. The following is an excerpt from a book manuscript of mine currently under review (dealing with the folklore of Cornwall - some of this excerpted material is specific to Cornwall, but it applies to the larger question of how these beliefs and the associated stories appeared here and there):
The first thing to acknowledge is that traditions about land-based supernatural beings, whether in Cornwall, Ireland, Sweden, or anywhere else in Northern Europe, drew on many shared assumptions. First people believed these extraordinary entities dwelt nearby. Reidar Christiansen observed that Irish and Scandinavian folklore consistently provides evidence that they share ‘a common background, the belief in the existence of a hidden race, living close to the human world, perhaps even under our very houses. As they are neighbours, contacts are inevitable, and as they are liable to be irritable, even malignant, there is always the risk of offending them. The fact that their reactions are unpredictable increase this risk.’ (Reidar Th. Christiansen, ‘Some Notes on the Fairies and the Fairy Faith’, Béaloideas, 39/41 (1971-1973) 95-111.) In addition, the Northern European supernatural beings are the subject of numerous legends. Many of these are shared across the region.
And also this:
Bo Almqvist addresses an issue in Celtic/Anglo-Saxon studies involving the question as to how much Anglo-Saxon culture, besides, of course, the language, survived the early medieval colonisation of Britain. He indicates that he agrees with the more modern thinking on this that the Anglo-Saxons gave as much as they took, creating a hybridised society and culture that serves as an analogy of what Almqvist spent a lifetime studying, namely the interaction of Celtic and Scandinavian folklore.
The Cornish naturally encountered not only Anglo-Saxons but also Scandinavians. Almqvist’s essay, ‘Scandinavian and Celtic Folklore Contacts in the Earldom of Orkney’, attempts to determine which elements of the respective traditions were borrowed and which may represent common inheritance. It is no mean task, but Almqvist writes with authority, having spent decades pondering the question and reading sources in multiple languages to sort out similar texts and their possible origins. It can be no surprise that the Cornish material should present a similar situation and problem. Cornwall cannot be regarded as the ‘Venice of the North’, as Almqvist characterises the medieval earldom of Orkney; nevertheless, the Cornish nation was something of a similar crossroad. While it retained its integrity in the face of medieval Anglo-Saxon advances, Cornwall offered less of a secluded hinterland than Wales or mainland Caledonia, which could maintain an insulated core culture. One would expect the Cornish to have had their own oral tradition before the many forces of history had their way. Regardless of how the factors that affected lives and culture played out, the folklore of Cornwall certainly had the same common inheritance that Almqvist suggests ‘is part of the explanation of the unity that exists today among the peoples of the British Isles’. (Almqvist, Viking Ale, 25)
Almqvist further writes that Reidar Christiansen, 'has pointed to a series of close parallels between certain Scandinavian and Scottish-Gaelic and Irish legends, and has introduced the term North Sea legends. It is not easy to account satisfactorily for these similarities. It may be that some of the motifs and legends are part of a common stock, but there can be little doubt either that the Norse and Gaelic speaking communities influenced one another, and that certain types and sub-types spread in either direction.' (Ibid., 27)