Baby's Weight 2.3kg At 31 Weeks

Gynae say baby is on the big side and ask me to cut down sugar and carbs. According to the scan baby's size is 2 weeks in advance! And because I'm on the petite side gynae say might be hard for natural delivery if baby too big. Feeling worried but dun dare to cut down too much food scared not enough nutrients for baby and sometimes will get hungry as well. But at the same time worried about babies weight at birth as c section takes longer to recover and also read about the negative future health implications of too large babies.. Any advice Mummies??