I think 2.74kg at 37 week is good, your baby will gain weight at about 3kg by EDD which is good weight for nature delivery.I'm 37 weeks now and I can feel the baby really low now. My last gynae visit last friday, he told me baby's head is already very low though not engaged yet. Cervix also not yet dilated. These few days, I feel on and off pulling sensations down there and a tinny winny bit of cramps. I am hoping to at least "dong" until 39 weeks before baby decides to come as right now, he's only at 2.74kg which gynae said is slightly on the small side. Hopefully he can gain a bit more weight in the next 2-3 weeks to come.
Did your gynea mention your baby face your back or front? I learn that if baby face front will have late engagement and delivery.