If you want to lose weight, the bottom line will always be calories, so if you're eating extra carbs to help with your runs, you'll have to eat less calories to balance it back out.
As was already stated, fats aren't as readily available for energy as carbohydrates, so they are ideal for low intensity exercise like walking and doing normal daily activities.
I am a bodybuilder (used to be a runner) - The most important time for a bodybuilder to take in carbohydrates is post workout because when the body is depleted it needs to absorb nutrients like amino acids. Carbohydrates increase insulin levels which in turn increases the body's ability to uptake nutrients. So, bodybuilders take in protein with carbohydrates post workout. The second most important time for bodybuilders to take in carbs is pre workout for all the same reasons that a runner takes in carbs before their workout.
Disclaimer...The following is just my loose interpretation of what's going on in your body during a run.
When you take off for a run and are full of nervous energy and maybe a little jumpy, you're running on sugar in the bloodstream. That doesn't last very long before you "settle into a pace" and start burning glycogen that is stored in your muscles when you eat carbohydrates.
When a runner "hits the wall" it feels like a sudden loss of energy as if you can not possibly go any further. I believe this to be the point at which glycogen has become depleted.
If you push past the wall and maintain a strong pace despite all the signals your body is telling you, you'll "get your second wind". At this point, I believe your body has transitioned from burning glycogen to metabolizing protein for energy. When exercising at a high intensity, fat is not as efficient an energy source as muscle tissue, so it is not likely that fat is being burned primarily.
Sometimes you can "hit the wall" again. If you continue to push past that for very long and get a third wind, you'll get "runner's high" which is your body releasing endorphins because that's all you have left to run on.
I miss runner's high.