Hum, I was 2 weeks late & about 6 lbs 10 oz. My brothers (twins) were 8 days early, & about 5 lbs each. DH & his brother were both about 7 lb at birth.
Anyway, my first two babies were about 6lb 12oz at 39-40 weeks (so fits the theory of genetics nicely).
Except my mother was tiny & a heavy smoker (whereas I am tall, broad-shouldered, never smoked, hearty eater & exerciser).
By the time I got to 3rd/4th babies, they were both exactly 8 lb 10 oz. And each time I gained the same amount of weight roughly as I had with first baby. Only difference.. 3rd-4th babies were 1-2 weeks late, not 1 week early.
So what I'm saying is, except for smokers, I think length of gestation is more important than anything else wrt baby birth weight.
Now, STRETCHMARKS, I am sure they're strongly related to how much weight mum gains, that makes a lot of sense to me.