I also remember reading something (long ago, so I have no sources and no notion whether what I read was reliable) that said that sleeping on the left side is also better for circulation. It had something to do with the heart being on the left side and gravity being more helpful when you slept on that side.

When I was preggo, my doc told me to sleep on my left side. I never asked why. I wonder if this was the concern. For what it's worth, I generally am a left-side sleeper (at least at the beginning), and I've never had issues with heartburn.