What is the purpose for walking (power walking for exercise) with hand weights? and does it achieve something? I have in the past done this, but can’t really say if it did anything, other than make my arms a little sore. Does it increase the heart rate? Increase arm muscle mass?
I don’t think you are doing anything but pulling on your shoulder muscles. If I’m picturing hand weights for walking, they are usually very light weight. Maybe if you did curls while you walked, you would be exercising your biceps, but, just swinging your arms as you walk? I don’t think there’s a benefit.
If you want to increase cardio, try a knapsack with a few 10 lb. plates in it.
That’s what I thought - but I continually see people out walking with hand weights.
A while back, someone invented an exercise regime called heavy hands (IIRC) which involved pumping your arms while holding weights. The author very specifically cautioned against just carrying the weights, claiming that that was not particularly useful.
It’s called the farmer’s walk . Powerlifters use it to train for grip, and it’s an event in strongman competitions.
Plus, if you’ve got a couple of years of training under your belt, walking around a parking lot with 100lb bells on each hand looks mighty impressive. 
An X-Vest is better cause the weight is more evenly distributed.
And I doubt most of the folks doing this are practicing for the farmer’s walk. The strongman event involves carrying 350 lb. “dumbbells” across the length of a football field for time. Powerwalking with a 5 lb. weight in each hand just isn’t good preparation.