I imagine there's some kind of effect but it's probably pretty subtle. Since our body changes orientation through space, my guess is there are mechanisms in place to make sure things grow in an optimal and balanced way and repair/defend against such things.
I'm not sure specifically what you're worried about, like the difference between sleeping on your back/side/front, or whether you're horizantal or maybe sleeping on an incline like some old folks do?
Or perhaps sleeping upside down like Michael Keaton in Batman? Gravity boots are pretty cool...
Old people stooping, I wonder if they could fix that with some traction like dips and chinups or inversion table.