LV and I will both answer the same here, but I got here first
basically, if you run first, you use up a lot of glycogen in the muscles, and that's what the body needs for weight training...so your weight routine suffers.
ideally, after weights, you wanna knock back roughly 20g of protein and 40g of simple carbs, no fat, no fiber. something to refuel muscles and glycogen stores.
The reason running after weights might hinder progress is it gives you more time to turn catabolic, which is a muscle wasting state. the post workout shake above will keep you anabolic...muscle building...instead.
I really prefer separate days for weights and cardio. When they are the same day, i advise something like morning cardio, evening weights (or vice versa).
Don't try to run the fat off. Doesn't really work that way. Lose the fat through a clean diet. Build muscle with a good routine and a clean diet, since muscle burns calories.