How much does your baby weigh?

Lish
I am 34 weeks 2 days and my baby girl is measuring 5lb 13 oz +/- 10 oz. My doctor said that is average weight for gestational age, but this seems huge to me considering I have between 3-6 weeks left. Her legs are long so I feel that is contributing, but is this normal weight for this time?? Does weight start to level off the closer you get to your due date?