Firstly, the theory of light weight high reps comes from the assumption that this can help you tone and striate the muscle. However, you cannot change the shape of your muscle, as your muscle shape is determined by your genetics. You can only make your muscles bigger or smaller, and you need to maintain their size by lifting heavy weights because lifting lighter weights means that you’re telling your body it doesn’t really need its muscle.
Next, emphasise diet over cardiovascular exercise. Even if you’re doing insane amounts of cardio, you won’t lose any fat unless you’re also cutting down on calories. You should be in a deficit of 500 calories daily if you want to lose 1 pound a week. It may sound less fun but think about it: would you rather do 50 minutes of cardio daily or simply cut out 55 grams of fat? However, some cardio is necessary; especially to maintain your muscles but 3-4 sessions a week will suffice. You can benefit from high intensity interval training (HIIT) because it’s brief if you’re short on time. However, HIIT requires high levels of energy, which may be in short supply if you’re dieting, so low intensity steady state cardio (LISS) may be a better option for you as it is easier to perform, though it takes more time.
So, in short, you don’t really need to change your muscle-building exercise routine if you want to lose fat. Remember that the weighing scale may not portray the most accurate results, as muscle weighs more than fat, but if you stick to these principles and ignore what the other sheep are doing, you can have the muscles you want and get rid of the fat that you don’t.