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The big thing you need to worry about is whether or not she's eating enough food. Drinking lots of milk provides a lot of calories and can make children full, which can often make them not want other food. As long as she is eating enough fruits, vegetables, protein and whole grains and is at a normal, healthy weight I wouldn't worry. Make sure you're diluting her juice with water so that she doesn't get too much sugar. That will contribute to weight gain more than milk.
Make sure it is low fat milk (1% or skim) and our doctor said our daughter should not drink more then 24 ounce a day. Which would be like 3 cups. I know my daughter will drink more if we give her milk. So we limit her milk intake. If she is really thirsty she will drink water. Milk taste good that is why they drink it so fast. You can look at your daughter and see how she looks. Make sure she is active and the rest of her diet is balanced. She is more likely to get fat from junk food then just milk.