Melissa Herrera, a trainer at my gym, made some additional comments about the aerobic activity of running and other reasons for doing weight training.  She says,

“A good way to use running as a part of your training,. . . is doing intervals.  Intervals are a good way to build up your endurance.  For example, start out by walking for 5 minutes, then running for one.  Maybe the next week you walk for 4 minutes & run for two.  Alternating the walk/run cycle and eventually decreasing the walk time down to zero to none.  {Another way that Weight training is} a benefit is that it helps boost your metabolism.  It does this because you are increasing your muscle and muscle is what burns calories, not fat.  Therefore, the more muscle your body has, the more efficient it can be at burning calories.  Cardio and  weight training are equally important when trying to lose weight.”