First, 12 inch biceps are NOT big. If they are jiggly, that's fat. 12 inches of muscle looks quite good.
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you would have to lift like it was your full time job in order to get your muscles really big
It pretty much is my full time job, and my biceps at their largest, flexed, are 12 1/2 inches. I curl 30 pounds dumbbells for 10 rep sets and can't seem to get them any larger.
Doing cardio with weights is a great way to injure your rotator cuffs. The difference in the number of calories you would burn is miniscule, but the chance of injury is very high. while you are doing cardio, you really can't pay attention to proper weight lifting form. In addition, if you do it too frequently (like everyday) you'll also have injuries. It's just not worth the risk of injury.
Pick a weight which you can do 10-15 repetitions of an exercise. It should be quite doable for the first few repetitions, then HARD for the last 2-3. 12 inches of muscular arm looks great, 10 inches of muscle with an inch of fat padding all around looks bigger

As Ilene said, you can't spot reduce. You can build muscle, and use nutrition and cardio to lose fat.
Mel