Aerobic exercise is great, but you shouldn't do it to lose weight. Do it for the benefits to the cardiovascular system. Anaerobic exercise will add muscle mass which in turn increases your metabolism. Also, by strenuously using your muscles every week, your body has to continuously repair them.
That is important because our bodies are designed for survival. What I mean is that when forced to lose weight, your body will first burn whatever muscle it doesn't need, then resort to the fat. It takes less effort for your body to break down muscle than fat, so it does so first. Your body puts a priority on repairing itself, so it's going to be forced to not burn the muscles it is repairing and instead break down fat for the energy it needs because you're eating less than you need to maintain your weight.
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