Ultimately it comes down to this: Calories = (proteins + fat + carbohydrates)
Weight = calories - (exercise + metabolism)
You can reduce your weight by reducing calories below what your body is currently using to lose weight.
Reducing carbohydrates for people with diabetes also has the added benefit of helping to reduce blood sugar.
However if you replace the calories you are saving by cutting down on carbohydrates with extra calories from fats and proteins you are not going to lose much if any weight unless you increase exercise and/or metabolism. Fats slow down digestion of foods so that the blood sugar is affected more slowly. Hormones do cause changes in metabolism and fat storage. Women of my age have to eat less or exercise more than they did at a younger age to maintain the weight they had at the earlier age.
Any method that supplies the vitamins, minerals, fiber and calories you need and motivates you to reduce caloric intake will result in weight loss. You will get a lot of support on this forum for using the low carb diet.