Mark Fenton says no. The benefits don't outweigh the risks. By using hand weights, you risk causing injury to your shoulders or the muscles of the upper chest.
To burn more calories when you walk, concentrate on moving your arms more vigorously. The weights might actually slow you down as you get more tired. Your arms will move more slowly and your legs will follow suit. Plus, forgetting the weights might just turn into another excuse not to walk.
Some people use long walking poles when they walk, much like a cross-country skier. These poles can increase the energy expenditure and they reduce the risk of shoulder injury. But you have to ask yourself, do you want more apparatus to carry when you walk? Sometimes the best aspect to walking is its simplicity.
If you really want to increase caloric burn when you walk, walk faster and move your arms vigorously.