A problem with using aerobics only for fat loss is the likely hood of muscle loss. Especially when doing high intensity aerobics which is very popular these days. Let me tell you why, If you do not include resistance training aka the weights to balance out your aerobic routine muscle loss will occur also reduce the need for calories. If your caloric intake does not balance out with the loss of muscle unneeded calories will be stored as fat.
So a person who only does aerobics can actually benefit from weight training with light weight and high repetitions. The reason is because weight training causes energy depletion within the muscle. As the muscles recover and start to adapt they will begin to store more energy allowing your muscles to last longer during aerobic activity. With the cause of aerobic failure being due to the exhaustion of blood, liver, and muscle glycogen ( sugar ) weight training could really help a person with their aerobic routines.