How do I Loose weight while marathon training?

The same way you lose weight when you aren't training...eat your net calories. When marathon training you don't need anything extra in your diet* except for carb replenishment when on long runs. Feel free to look at my diary, i'm training for a series of half marathons and im losing about a pound a week.

*this is assuming you get adequate protein, carbs, and fats in the first place. I use a 35%, 50%, 15% ratio respectively.

Last year I attempted to lose weight while training for a half. Bad idea in that I went for too high a deficit, even eating back exercise cals. I bagged it and just ate what I wanted. After the race I continued running and tweaking out my diet. I needed a very small deficit to lose, and I did. Right now I am training for a full marathon but I am in maintenance.

My coach always said I shouldn't try. Even though it made sense to me that I would do better if I was lighter, he swore that the fuel was the key thing with marathon training and I could lose weight some other time. You can probably run a deficit on long run days, because it's hard to eat all those calories back (not that I didn't try, and, sometimes, succeed), but the day after you run long you will be starving and need way more than 1200 cals. Sorry to be a downer. You can watch intake closely, try to stay around 1200 net, and if you are more disciplined than I am you might be able to lose slowly, but I never could lose more than a few pounds when training. Just my two cents.