I'd advise against carrying weights while walking. Joints are generally designed to be compressed not stretched, and having to arrest the momentum of the weights with every stride stresses the joints in ways they were not meant to be stressed. There is a reason "The Rack" was a medieval torture device.
If you do want to carry extra weight to increase the intensity of your walking, use a weight vest or backpack, which keeps the weight close to your center of gravity.
Also, strength training is effective only to the extent that it is genuinely challenging your muscles at close to their maximum capacity. This is generally taken to mean fatigueing your muscles in 15 reps or less (ie. 1-2 minutes). If you can carry something for 20-30 minutes of walking, it is simply not challenging enough to develop your arm muscles. If you want to develop them, lift heavy with dedicated strength training.
The reasonable man adapts himself to the world; the unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man.
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