Sort of? Personal fat threshold doesn't even require a person to become obese or even overweight. People with the sort of dyslipidemia where they can barely even accumulate normal fat tissue can get insulin resistance/type II diabetes. It isn't so much the fat as it is the fat showing up at the wrong time, in the wrong place. I don't think there's any question that obesity can contribute to diabetes. A might cause both B and C--that doesn't mean B doesn't increase C and vice versa.

Robert Lustig has compared fructose to a high fat/high carbohydrate diet. It does seem to worsen the effect. The liver is exposed to increased carbohydrate metabolism--but without the insulin response, fat metabolism is not adequately decreased, so maybe you get this mix of the two. I do think this is a case where fructose can both increase obesity and increase insulin resistance and risk of diabetes--so both having a single cause. But that doesn't mean that the weight gain itself can't make things worse and still contribute to the development of diabetes. The most fattening diet for rodents isn't necessarily high fructose, fructose is mostly used in the diet for models of insulin resistance/diabetes.

I haven't seen anything showing that once a person is insulin resistant, with higher peripheral insulin, they're more easily fattened. Or I don't think I have, maybe I missed it. I've seen claims, theories that that's the case. I think it's more likely it's harder to get fatter at that point, although of course you can blow through stalls with exogenous insulin and various diabetes drugs (they call the weight gain a side effect, but it's probably pretty much the very mechanism by which they have the desired effect).