Is brisk walking enough at 52 or do I need to start weights as well?

My daily walk of 40 to 45 minutes has become a habit now. My sugar readings have improved and I have lost about 4 kg since May. However my son, who goes to the gym, insists that I must also do some strength training because muscle helps with insulin. My doctor has not said anything against it but also has not recommended it. I have never lifted a weight in my life and the gyms in my area are full of young boys. Is there something I can do at home safely at my age? I do not want to injure my back which already troubles me during the monsoon.