You can be normal weight but you can't be healthy. Carbs are themselves toxins, humans never evolved any capacity to consume a significant amount of carbs in the diet. No indigenous diets are high carb. Not only that but most carb rich wholefoods contain huge amounts of anti-nutrients, fiber itself is an anti-nutrient (it inhibits absorption of nutrients and damages the gut).  It's counter-intuitive but the least harmful way to eat a high carb diet is processed carbs like white rice that are very low in anti-nutrients. Eating whole plant foods in any great quantity is going to result in serious health problems.