When I begin to paint weights for arms/legs, it paints the same side weights on the other side instead. It mirrors the same weights. My mesh is symmetrical butt I also check it by doing edit mode and symmetrical. Also, I've tried keeping on/off Auto Normalize but I would get the same results. Thinking it might be my mesh, I made a new scene using the default cube, used a mirror mod(applied it), created some geo/bones, and repeated the process. The same thing happened, so I'm not sure what could be causing it. Here are some images to give you an idea. And the brush settings are default "mix."
There are two different symmetry options while using wheight paint:
Symmetry 1 mirrors the strokes along X axis in the active vertex group. Symmetry 2 mirrors the strokes on two vertex groups which have the same name and suffix like .l .r, .L .R, .left .right, and similar (check Blender manual for a list of valid suffix).