The balance system is complex and in fact involves 3 major sensory input systems, all controlled by the brain. The inner ear sensors for balance, eyes and the proprioceptors on the body all send information to the brain. Balance centres receive, analyze and integrate these bits of information and then send orders to the body to readjust according to the movement done in the first place.
When you are dizzy with computer use, it usually means that the balance system is relying more heavily on the visual input. It is not fully reassured by the inner ear sensors telling them you are not moving. You can read more about it here: https://balanceanddizziness.org/do-you-get-headaches-or-motion-sickness-from-playing-computer-games/
Having the weights on you or changing your posture as you walk is increasing the cues coming from the proprioceptive system to the brain. This additional input seems to help you balance.
I would recommend you to have your inner ear sensors tested. It might be that they are working just fine but your centres in the brain are not using their information properly or it might be that your brain is in need of all this additional information (visual and proprioception) because your inner ear sensors are dysfunctional.