The only advantage to exercising while carrying weights is that you can get more exercise while moving slowly. To strengthen your heart, you have to exercise vigorously enough to increase your heart rate at least 20 beats a minute above resting. How fast your heart beats depends on how much blood it has to pump to your body. When you run and carry hand weights, your heart has to pump blood to your exercising leg muscles and also has to do extra work to pump blood to your arm muscles. That means that you can achieve the same heart rate when you run more slowly.
Competitive runners should never carry hand weights. How fast you run in races depends on how fast you run in practice. Carrying hand weights slows you down, so you become a slower runner. Carrying weights also interferes with the natural motion of your arms while running. On the other hand, carrying weights can help to protect people who develop frequent running injuries. Carrying hand weights slows them down, so less force is directed at their leg muscles while they run. Hand weights will not do much to increase your arm strength, because to become stronger, you have to lift progressively heavier weights.