No, heavier BBs don't have any effect on the gun itself.
Bio BBs tend to be banned at most fields because they often shatter into dust which has actually gotten into some player's goggles and caused serious irritation to their eyes. I was witness to one. Also, bio BBs tend to have a limited shelf life, often come in a sealed package that expires in a few weeks after opening. Bio BBs are rather like Kraft Cheese Slices that reduce to powder if they hit something hard like plastic.