It may be observed that in this book as in The Hobbit the form dwarves is used, although the dictionaries tell us that the plural of dwarf is dwarfs. It should be dwarrows (or dwerrows), if singular and plural had each gone its own way down the years, as have man and men, or goose and geese. But we no longer speak of a dwarf as often as we do of a man, or even of a goose, and memories have not been fresh enough among Men to keep hold of a special plural for a race now abandoned to folk-tales...
The Old English was dweorġ, dweorh. The plurals were dwerwhes, dwerwes, dwerows, dwarrows (similar to how Old English beorġ became barrow, burrow) so Tolkien's right, the plural would have been dwarrows if it hadn't been regularized to dwarfs.
Its use in English to refer to the mythical beings doesn't happen until 1770. It seems that the Vikings were much more familiar with the mythological creatures. The Old Norse cognate dvergr is found in place names, like the Icelandic town of Dvergasteinn. An Old Icelandic word for "echo" is dverg-mál, literally "dwarf-talk" from the belief that dwarfs lived in rocks.
The etymology of dwarf is uncertain. The OED reconstructs a Proto-Germanic form *đwerǥoz and an Indo-European form *dʰwérgʷʰos. It connects the IE root to Greek σέρφος (from *τϝέρφος) "midge". Porkorny suggests either *dʰwergʰ- "low (in stature), crippled" or *dʰwer- "to ruin by deceiving", which is related to *dʰreugʰ- "to deceive, harm". If it's from the latter then it's cognate with dream (from the Germanic suffixed form *drauǥmaz). Old English drēam meant "joy, music" and the modern word "dream" was influenced in meaning by the Old Norse cognate draumr "vision, dream" (AHD).
Arnold Zwicky has more on dwarfs/dwarves.