diabetic cat question

My 11 year old cat was just diagnosed with diabetes 6 mo ago. He also may have cushings disease. He gets reg insulin and levemir. He eats boiled chicken breast mixed with a spoonful of canned friskies, so its mostly chicken. He eats dinner around 5 pm. I check his blood sugar before he eats and give him reg insulin as needed. Before bed i check his sugar again and its usually 60-100. My question is how does his sugar rise to 200-300 by morning? I am stumped as to why this is happening. Im trying to get him off the insulin but his sugars are still so high with very little carbs. I would appreciate it if someone has an answer for me.
Thanks ahead. Dawn