I don't know enough about Jaimie's twin Jessica to know if she's as low-wattage as Jamie. All I do know is that Jessica had cancer in early childhood (which recurred at age eighteen, and that shit is rough on not just the patient, but everybody in the family. On top of that, they also have an older adoptive sister who ended up an addict, who Jaimie blames for "ruining the family," when what really happened is the older sister had to deal with the arrival of much-wanted twins who were the "real" kids in the family, and probably started acting out because of that dynamic. Jessica's cancer would have exacerbated that.
If you're the sibling of a child with significant medical needs, it's all too easy to end up not getting your own normal needs for attention and nurturance met, and to feel like you're on the periphery while all the adults' concern is channeled toward your sick or disabled sibling. You're not allowed to have problems (much less be a problem), and if you do, they're minimized or dismissed outright because they're not [serious medical condition].
It's fucked up, and a lot of people just don't have the psychological insight or emotional resources in that situation to help their not-sick kids navigate it. Grandparents who are wise enough to see what's going on and make extra time to help the not-sick kid through it can help tremendously, but it doesn't seem she had that. It can be even rougher when the family is short on funds and a kid's material needs are also de-prioritized in favor of their sibling, but even in a wealthy family it's hard.
Hell, a similar thing happens when one parent has medical or psychiatric issues. (See: Holliday, Tess; O'Brien, Anna.)
Either way, turning to food for solace is a common maladaptive behavior, because if adults or older siblings can't help a kid get their emotional needs met, they're going to find a way to self-soothe. Eating is one of them, and it's so primal, it's easily accessible to a four-year-old.
That her father is a successful entertainment lawyer tells me that her parents were very concerned with appearances, so Jaimie getting fatter and fatter would have been a major bone of contention. Wanting to get her WLS at 13? I can believe it. They already had the adoptive older daughter who no doubt was acting out by various means even before she turned to drugs, and she was probably the family scapegoat (thus, she's the one who "ruined the family" in Jaimie's estimation).
Jaimie is still that four-year-old who didn't get her emotional needs met at a crucial time, because everybody was focused on her sister's cancer, plus her older sister's acting out her own pain. She was too young to make sense of it, so she did what she could to feel better, and that was eating. Nobody saw what was happening, recognized it for what it was, and got her or her older sister the help they really needed at the time when it would have done the most good, and Jaimie has never developed the self-awareness to recognize what she was doing to herself as she got older and turn it around on her own. She may even have doubled down on the eating out of buried rage against her parents, because she could potentially have gone the other way and developed anorexia as a way to be perfect for them and regain their love, had she thought that was attainable.
I think Jaimie's parents have simply given up on her. They've moved her out of their house and are subsidizing her existence because they can't or won't see how they failed her (or her older sister), and the guilt, shame, and humiliation of facing her in their home every day is something they don't want to deal with. If you ask them, they'll no doubt tell you they love her and they've done everything they can for her—and that's probably true. Having enough deep empathy to recognize how she got this way in the first place may simply be beyond them.
Day in my Life 
