with my first pregnancy I was vegetarian, I started at 5'3"/101lbs. I gained 40lbs and gave birth to a 6lb 10oz baby girl at 38+5. lost all the weight by 3 months PP
with my second I was vegetarian to start, but started eating meat in the first trimester. I was still nursing DD. again started at just over 100 lbs. I gained 50 lbs and gave birth to a 8lb 9oz baby boy at 41+3. only problem giving birth to my "big" baby other than a slight sticky shoulder, that my midwife was able to unstick in one contraction (though the shoulder did click for a week or two)
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I think the high weight gain=big baby thing is only true when caused by gestational diabetes or a high sugar intake. as long as you aren't overdoing the simple carbs and are getting enough protien and fat, you should be fine. and I would totally think about switching care providers.Â