You can actually get diabetes if you're way overweight... but being overweight isn't an automatic diabetic ticket... you'll need to have some genetic predisposition to getting it, at least.
Living without sugar or with minimal sugar in your diet is ridiculously...
ridiculously easy. I'm diabetic and I haven't had to have a single shot of insulin in five years (I check regularly and go to my doctor every six months). I got it by working nearly 24/7 one summer and drinking way too much Coke as a means of rehydration. After losing weight and going on a no-sugar diet, I was able to kick insulin after a month, and I'm now up to the point where my sugar will only spike if I eat a honking big steakhouse meal or down a pint of ice cream.
However, I
do have a family history of diabetes... so one day, it will get worse. Until then, though... I enjoy being as healthy as I can be.
The only sweets I have are diet sodas (which I'm now limiting because too much soda is bad for you...) and the occassional sugar-free dessert or ice cream (once a week or so).
I've gotten to the point where I actually get a queasy stomach if I eat something dripping with refined sugar.

Seriously... the stuff is disgusting.
You don't need so much sweet in your diet. Just a little taste of sweetener now and then is enough... the new ones are so good that you don't think about it, anymore... many have no aftertaste at all... but they cost like hell. I suggest you save them as treats on days when you have been exceptionally good.