I have no answers to most of these questions. I can share my personal family experience though to add one more data point if it would help.
My father and his sister are both obese, and my sister is borderline between overweight and obese (about where I was before I started losing). My mom had been overweight but recently lost it -- she was never overweight until after having kids, and never as severly as my dad or me & my sister. My mom's family varies from normal range to very slightly overweight. My dad's mom was overweight when she was younger and became thin as she got very old. Of my two cousins on my dad's side, one has always been normal weight, one was obese and then lost the weight after her divorce. Her two kids have varied from normal to slightly overweight, never more than that. So there is the nature part.
As for nurture, food has always been HUGE in our home, especially among my dad's family, who I grew up with. Every family event involved a big dinner, the more special the occasion, the bigger the dinner. Every good thing was celebrated with food and every bad thing comforted with food. If I see my parents after a long absence, I don't hear "I love you," I hear "Where do you want to go for dinner?" They mean the same thing in my family. This is why I have such a hard time believing that environment could possibly play such a small role.
Aside from the issues about emotions and food, we also went out to eat multiple nights a week (especially after my mom started working full-time when I was in high school), always had dessert on hand (the only rule about dessert being that we had to eat a piece of fruit before we were allowed to eat dessert, but that rule magically vanished once we were old enough to get food for ourselves), and ate lots of high-fat meals. Once, after I had lost some weight, I went home to visit and offered to cook dinner. I cooked a chicken stir-fry and served it with rice, and my dad's comment was "It's not fried!" I think he was joking, but seriously any stir-fries he ever cooked had the chicken fried first (they were delicious, btw). Our eating habits were terrible. Fast food multiple times a week, dinner out multiple times a week, lots and lots of prepared foods. "Exercise" was always a dirty word. Breakfast on the weekends was IHOP or Jack in the Box. Yes, we did eat better when I was a little kid. But really, I have very few memories of that, and a whole lot of memories of eating junk when I was in high school.
After learning those eating habits as "normal," I feel like it's no surprise that I ate way too much junk in college. As part of my weight loss journey I have had to learn what "healthy eating" means. No, I was never taught it in school. I had seen the food pyramid but that's about it. It never occurred to me that eating out all the time was unhealthy, or that I ought to be exercising, or that dessert every night could be what made me fat. I told myself "I just come from bad genetics" and used it as an excuse for being fat. When I nearly failed gym class I said "Oh, I just have bad genes, that's why I can't run an eighth of a mile without getting out of breath."
Maybe if I had been eating and exercising like I do now my whole life, I would have been fat anyway. I don't know. But I find it really hard to believe that the environment I grew up in didn't play a huge role in my obesity.