Is my newborn gaining excessive weight?

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I know it sounds crazy... But My 2 month old baby has doubled birth weight already.

Doctor told me to feed only on demand. Baby is exclusively breast fed. I feed the baby when he cries at night. in spite of weight gain, Baby still sleeps for 2 hours at a stretch, not beyond that.

Is this normal? I am worried about baby not sleeping longer stretches and the excessive weight gain. Any inputs would be appreciated.

Thanks !