I know multiple people with type two diabetes who aren't overweight. They have good genes with regards to weight, yet bad genes with regards to blood sugar. One of these people runs every day.

Carbs are not bad for you in moderation, but if your body is drowned in them you can easily develop blood sugar problems, especially if you're predisposed to it. Otherwise, if you're highly active and aren't constantly eating more calories than you burn then of course you will have a healthy weight.

I'm not being anti carb or anything. It's just waaaaaay easier to cut them out, lose a bunch of weight, then reintroduce them in moderation, than to try and burn off an excess of calories each day via intense exercise.