Check your settings carefully. The only time I ever have one come out larger is when the bitrate, video or audio, is larger than the original.
Surprisingly from my playing resolution has very little effect on actual file size.
For HD movies i have on my computer in .mkv format, will those be able to play?
I don't think mkv files will work. MKV is a container kinda like AVI that holds the audio and video tracks. You'll need to use some software like "MKV extract" to pull the tracks and remux them into a .mp4 file.