Very interesting observation! In order to keep balance, our brain collects information from the vestibular system (the inner ear balance sensors), the visual system and the proprioceptive system (the sensation coming from skin, muscles and joints). The brain analyzes these three “buckets” of information to figure out what the body is doing and to send orders back to the body to adjust and keep balance. When you are carrying a heavy object, either on one or both hands, you are “enhancing” the cues from the proprioceptive system going up to the brain. From your report, this seems to help your brain to adjust more easily and you to feel more balanced.
This principle, as a means of strategically calculated and positioned weighted vests, has been used in balance rehabilitation of some central nervous system balance disorders, such as Parkinson’s Disease. You may wish to explore this option with your health care professionals team.