It depends on the cause of the high birth weight. I was over 9lbs born but my mother was 2 weeks overdue, which explains that, and I've never really struggled with weight.
But if the high birth weight is due to gestational diabetes then it is quite possible that there could be an ongoing struggle with weight. Gestational diabetes is a condition in which a woman without diabetes develops high blood sugar levels during pregnancy. Gestational diabetes generally results in few symptoms; however, it does increase the risk of pre-eclampsia, depression, and requiring a Caesarean section. Babies born to mothers with poorly treated gestational diabetes are at increased risk of being too large, having low blood sugar after birth, and jaundice. If untreated, it can also result in a stillbirth. Long term, children are at higher risk of being overweight and developing type 2 diabetes.