It may be a bit difficult to lose weight with hypothyroidism and diabetes but not impossible. 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. The key is to follow a healthy diet plan with a balanced amount of physical activity. A healthy diet should consist of adequate calories according to ones height, weight and physical activity; with adequate amounts of carbohydrates, slightly increased proteins, little fat and plenty of fruits and vegetables to supply vitamins and minerals. Start with a healthy breakfast, moderate lunch and light dinner. Also keep a track of calorie intake and your work out. As far as the physical exercises are concerned best results can be obtained with rotating between various activities like gymming, running/ jogging, yoga, pilates, aerobics, biking, swimming etc. With gradual consistent efforts, you should be able to lose weight in a healthy way.
Hope this helps.
make sure your thyroid levels are optimal - middle to upper 1/3 of range for FT3 and FT4.
Would say low carb diet would give you best prospect for weight loss. Should also allow you to reduce your insulin dose a little.
Could refer you to the book 'diabetes solutions' by Dt Richard Bernstein as best source of info for this approach - and for managing diabetes.
Please let us know how you go.