I don't think it's true mainly cause I was born 4lbs 11oz and yet I'm 37weeks with my son and he is already pushing 6lbs. As the ladies stated above, every baby and pregnancy is different.
It's all up to your baby! I don't the size you or your partner where at birth matters.
As for the movements, usually for your first baby people will tell you anywhere between 18-20 (maybe later), but this is my first baby and I can feel slight movements now at 15 weeks... It completely depends on baby and you :)
I'm not sure about how big the baby could be I think it would just depend on your body and what you eat. And I started to feel my baby's movements at 19 weeks but everyone is different .