Hi Patch,
Carbohydrate sensitivity is an interesting and fairly new idea. I'm not sure whether it has been scientifically proved or whether it is just hypothesis. The basis is that with increasing consumption of packaged, refined and sweetened foods over the past decades, there has been a corresponding decrease in consumption of whole, unprocessed foods. Eating a diet that consists of heavily refined foods, which includes a high-carbohydrate content, causes weight gain and eventually carbohydrate sensitivity. Once you become carbohydrate sensitive, your body can no longer burn fat effectively, and even moderate to low GI foods as well as complex carbohydrates get stored as fat.
So, to answer your question, being overweight does seem to lead to carbohydrate sensitivity, but this can be overcome by a reduction in carbs. Once the weight has come off then it is possible to eat more carbs, but if these are refined carbs then all that will happen is that the carbohydrate sensitivity returns, together with weight gain yet again.