@QAQTAT
kind of going backwards through the thread, so forgive me for that.
Stages are roughly neutral when full and positive when empty. When full, they will cause you to want to list to the left a bit because they are negative and hanging, and when empty they will cause you to list to the right a bit because they're pulling your left side up. This is typically not enough to be really noticeable when you are experienced with doubles. Unless I am focusing just on the stages, I don't notice and my body will automatically compensate by adjusting one of my legs just enough to balance back out and if it is particularly egregious, you can pack air into one of the sides of the wing and fix the roll that way. We are talking 1-2lbs positive or negative per stage, so it's functionally irrelevant.
Doubles will ALWAYS be unstable when you are rolled all the way over on your side and there is nothing you can do to really fix it. The scuba rig is negatively buoyant, the lift is in the middle, and your body is positively buoyant. You will roll over. Over time you can learn to manage it with some creative leg positioning and various muscles in your core. Yes, you can roll and pitch over just by flexing certain muscles in your body even though didn't "move" any of your limbs. Certain tanks will make you want to roll harder than others, but they all will, so best to learn how to deal with it which will only come with time and practice.
In terms of the harness. Should straps loose! They need to be loose for safety and comfort. A consequence of that is that when you roll you will feel the whole rig move. When you are in trim, your body is floating up against the backplate and you are pinned to it. Your waist strap is doing all of the work to keep you and the rig attached. When you go head down, you float up and the crotch strap engages to keep you in place. When you go head up, the shoulder straps engage to keep you from floating away. If you are regularly spending time on your side, a harness like the Transplate will let you use a chest strap and can be fit fairly snug to help prevent that movement, but you should not tighten a one-piece harness to the point that the shoulders are snug. You should always be able to easily get a fist under the straps.
Any lead added to your body instead of the rig will work to help lower your center of mass and center of buoyancy which will help to improve stability.