Yes it does, but I'm not sure you should be running if you're carrying a lot of weight.
Running creates a lot of bounce, due to all the impact. All the areas of your body carrying that excess will be subject to the skin being stretched (just a little) every time you jolt a foot down.
My personal favourite is power-walking. You will receive a good workout if you keep up a fast pace, there will be much less fat / skin bounce. Particularly though, power-walking is far better on your joints.
The most important aspects of all, is what you eat, when you eat and the quantity consumed.
High impact / energy workouts actually make you feel hungrier. Low impact workouts will get you more toned, lower the risk of injury and enable you to maintain a healthier food intake.
I highly recommend you eat nothing at all for the last 2-3 hours before going to bed. Just have water if you're thirsty, but not so much that you have to keep getting up to pee during the night.
Your body should be able to fully rest without having to digest recent intake of food.
Especially that last two hours before going to bed. Anything you eat in that timeframe has a decent chance of being added to fat stores within your body.