I am a side sleeper as well, both left and right. My stoma is on the left side. Yes, the bag flops around a bit as it fills at night, but I've never had a leak issue from it. I typically wear loose fitting pajama bottoms, which seem to give my bag just enough support.

Posted by: @rick

 I can get away without emptying thru the night if it wasn’t for the constant tugging..any suggestions?

Even if you could, it may be risky if your bag is filling up with output (or gas) overnight. The pressure and weight on your wafer may cause a leak or worse. 

I'm also a side sleeper and provided that I do empty my appliance at least once at night, I find that I don't have leaks or problems with tugging, although, I've probably gotten used to any tugging after this long. 

I used to wear something like a stealthbelt or similar support garment at night, which did give better support, but I found that it also reduced the capacity of my bag, effectively causing it to fill faster.

Some people do switch to larger bags at night, which is easy if you have a 2pc system. But that's not something I've done as my bag doesn't fill that much at night to justify the larger bag. 

I can only sleep on my side and have found that sleeping with a body pillow helps to add support to the pouch overnight.

Hope that might help!