If your going to gym, you might also be building muscles, so your weight won't change. A balanced diet just doesn't mean carbs and fruit, it's important to incorporate all parts of a diet, even healthy fats, this will also prevent cravings for bad fats (not saying you should pig out on even good fats though) . Maybe just make sure you eat a good/ large breakfast, and nutrition small meals throughout the day- dinner should be the smallest.
I'd also strongly suggest investing your time in cardio. This will help burn fat, but also help your heart whereas gym if often primarily strength training. Just start with something your comfortable with: swimming, running, biking riding, walking
If you are aiming at losing weight, it is important to calculate your current BMI and the target BMI. The target BMI should be in a healthy range. Aside indulging in moderate amounts of physical exercise it is also essential to maintain a healthy diet plan. A healthy diet should consist of adequate amounts of calories with carbohydrates, proteins, fat and plenty of fruits and vegetables to supply vitamins and minerals. Skipping any of the food components is not considered healthy. Also when aiming at losing weight the protein intake may be slightly increased and the carbohydrate intake slightly lowered. The calorie requirement should also be adjusted for ones physical activities as well. Lower than adequate calorie intake can also cause weight gain, due to the stress hormones kicking in. Start with a healthy breakfast, moderate lunch and light dinner. Also keep a track of calorie intake and your work out. With gradual consistent efforts, you should be able to lose weight as desired in a healthy way.
Hope this helps.