The BMI scale is much different for children. 70 lbs would be a very healthy weight for a little girl who is only 4'7''Oops. It's still a BMI of 15.3. For comparison, that would be like a 5'4" person who weighs 89 pounds. Picture that!
At 5'4" a weight of 108 - still very slim - is the bottom of the normal range on the BMI scale. The child of 4'7" should weigh at least 80.