For example, it may not feel like much, but long term use additional weight can cause injury with improper posture.
Walking in ankle weights can force you to use your quadriceps more than your hamstrings. It sounds harmless, however this imbalance opens your body to more injury potential while it attempts to compensate. This is especially an issue in the knees, hips and back.
The same is observed for arm weights. With improper form, or long term use, arm weights may increase your risk of trauma to elbows, neck, and shoulders.