Personally, I am not a fan of wearing weights while walking or running. When you start a walk/run, your blood pressure will be elevated due to the increase in body temperature and the activity you are about to start. By adding resistance, you may be increasing you blood pressure even further which may put you at a higher risk, if you do not pay close attention to your body and how it responds to the effects of added weights. However, as long as you monitor your vitals then going for a walk/run with added weights can have some benefit. I do believe your biggest benefit would be to complete your walk/run and if looking for added resistance then complete some strength training following your aerobic activity.
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Important: This content reflects information from various individuals and organizations and may offer alternative or opposing points of view. It should not be used for medical advice, diagnosis or treatment. As always, you should consult with your healthcare provider about your specific health needs.