"But doesn't determination to resist this urge to eat come into it too?"
Certainly and a surprisingly huge amount of that is due to brain chemistry. We all know that willpower is a challenge (don't need to be a scientist!) and that anyone who wants to lose weight will have to permanently keep their eye on the ball to keep it off.
"I'm confused - does this obesity gene mean that you want to eat more than you need, or that you eat the same amount as other people but you store fat instead of burning it off? Or both?"
There are numerous 'obesity' genes. The most famous one (if you are in to that sort of thing) is the FTO gene which actually only makes a couple of pounds difference, so there are lots of different genes, most of which we probably haven't identified yet. They probably have lots of different effects from making you fidget less, eat more, store fat in the 'wrong' places. Get lots of them and they cause more problems.
"If she read some of the views on this thread which suggest that weight is probably beyond anyone's control I think it'd have a seriously bad effect on her. I don't want her to believe that exercise and a moderate diet won't help or aren't achievable for people who have a genetic propensity to obesity, as she may well do. :-("
It isn't "beyond anyone's control" but there is a big genetic part of it that can't be ignored.
We tell everyone that a healthy balanced diet and exercise is the best thing and the most important treatment. The genetics isn't an excuse to avoid a healthy lifestyle sadly!
Exercise reduces fat in the muscles so reduces insulin resistance, reducing the chances or severity of T2DM potentially. Patients with a genetic predisposition to obesity need to be very aware that they must watch their diet constantly because it is going to be so easy to put weight on.
Patients who want to can, but you just need to watch an episode of 'Secret Eaters' to see how much we all delude ourselves about what and how much eat, so we all need to take responsibility for ourselves in that regard.