There’s not much research out there regarding type 1s and weight loss, but if you look at general weight-loss research, limiting calories (whether you limit them overall, or from a specific nutrient group or food group) is what works. Of course, just concentrating on calories and not considering food and nutrient groups doesn’t exactly help with hunger or other issues such as high cholesterol and high blood pressure (which PWDs type 1 or type 2 should watch as part of reducing risk of complications).
Drastic regimes may drop pounds fast, but if you want to drop pounds forever, learnings from organizations like the Weight Control Registry may help. Here are some examples (some weigh-loss programs, such as Weight Watchers, include some of these):
Daily physical activity is important: 30 minutes daily just to be fit, 60 minutes daily to aid in (but not guarantee–cutting calories not just burning them is key) weight loss. Keep a daily food journal. Regularly weigh yourself (but not obsessively!) Find in-person or online specific weight-loss support and counseling, in a group or one-on-one. Watch less TV.
Although insulin can contribute to weight gain, it doesn’t have to if calorie intake/energy output are balanced (eating enough calories to fuel your body and activities, but not more than that). Of course, the very tricky thing is to figure out calories/energy needs as an individual, eat that way day in, day out, and add the additional juggling of meds, blood sugar lows, etc.! Best wishes.