I recently switched my camera from saving in RAW to saving in Medium Raw. File sizes on the memory card are about 20meg a piece. After lightroom converts the files to dng, they have approximately doubled in size. Why is that happening?
It depends on the options you chose for conversion. Full size embedded preview in the DNG versus smaller one in the raw file? Include raw file in the DNG? Review these choices.
Also consider that it might not be a great idea in the long term to choose Medium. You're trading off the size of the embedded JPEG for disc space but for instance, apps that read the embedded JPEG would benefit from full size previews. Disc space is cheap.