Hi Milja,
If you use insulin, then achieving weight loss usually requires reducing your insulin requirements without compromising your BG control. In practice this often means reducing carbs and perhaps also protein intake (protein breaks down to sugars and amino acids during digestion) in order to be able to safely reduce your insulin. Regular aerobic exercise and perhaps using metformin can increase insulin sensitivity even in Type 1s.
Our bodies only start burning fat stores once all glucose stores are depleted - keep carbs low and try decreasing protein and increasing the % of fat in your diet, but as others have said, total calories do count - reconsider your portion sizes as well?