You probably won't need a c-section. I know women who gained 70 or 80 pounds during their pregnancy and gave birth naturally. Don't worry too much about the weight gain the most important thing is that your baby is healthy. I feel like I'm gaining too much weight too. I'm 15 weeks and have gained 12 pounds but my doctor said because of my height, I'm 5' 11, and my weight before pregnancy my weight gain is fine.
Also with the big baby thing my sister was almost 11 pounds and my mom delivered her and didnt even tear. I only say its probably not from the baby because you said the dr said you are measuring fine
You can vaginally deliver a big baby but the weight is most likely not from the baby, you could be putting on weight in other parts of your body. If its easily distributed then it wont be as noticeable. My dr said the same thing but im actually measuring small. Ive put on some weight around my bust area but not in my boobs really ive only gained half a cup size but went from 36 to 38 around ive also gained a little in my hips. But its so subtle and evenly distributed that no one can really tell. I only know because my clothes got tighter in those areas.