Did you ask your gynae what percentile your baby is at? Or did your gynae flagged out anything? If your gynae did not flagged out anything, then your baby is at the safe range.
Babies will grow faster at the last few weeks of pregnancy. Don’t worry! Just make sure you have been eating well and consume your supplements daily.
My baby was also small and light at first but grow a lot faster at my last few weeks of pregnancy.