Honestly, it's a crap shoot!
I'm a plain ole white gal, had twins that were over 6#'s each! Stretch marks and loose skin up the wazoo. However I was not overweight at the start.
But then, my aunt had 2 babies, 2 different times, both 9/10 #'s, not a stretch mark one. She was really thin. But, she is half American Indian, half French.
My "girls" went "SOUTH"! My sisters, not a droopy bit! *rolls eyes*
Focus on your health! There is no way to predict, how pregnancy is going to affect you. Until you've been there, done that!
Being pregnant was the strangest time in my life for me, because my body, just did, WHATEVER, and I had no control.
To your original question, medical technology has come a long way, and in that respect, you will most likely be ok. However, the healthier you are, the better the pregnancy will go, and delivery will be easier.
If I were in your shoes, I would get the family complete, work on a healthy lifestyle, and then, consider the skin surgery. I don't see much reason to put the cart before the horse.
Good luck! Enjoy the ride of parent hood! It's awesome! Grandkids are even better! Love all 4 of mine! Totally worth it!