These are two separate issues. As a diabetic you should keep your BG in range as much of the time as possible. It is fine to eat different amounts of food on different days as long as you cover the food you eat every day to the best of your ability.
Weight is determined by the total number of calories you consume vs. the total number of calories you burn. If you eat fewer calories than you burn for the week, then you will lose weight; if you eat more calories than you burn for the week then you will gain weight; etc.
You will probably find it is easier to cover the food you eat with insulin if you make your food intake similar from one day to the next simply because it is more predictable. But it isn't necessary for either blood sugar control or for weight management.