You have to be very careful about exercise with dogs that are severely overweight.
I would cut his food down a little more and encourage him to be more active.
When he is slimmer you can increase his exercise, but i would have him checked by a vet first.
You want a slow and steady weight loss. How much does 1/3 of a cup actually weigh? For an overweight dog you want to be feeding less than 3% of his ideal body weight, not including veg. So if his ideal weight was 4lbs, he only needs about 55g (raw weight) max of meat a day. (That is 3%, some dogs who are prone to gaining weight may need as little as 1.5%) You can give extra veg to fill him up
It is easy to overfeed by a small amount every day unless you are weighing his food
Make sure he isn't eating any kibble at all. I would then split his food into several small meals.
Make sure you aren't giving any starchy veg (all root veg, peas, beans, squashes) or high sugar veg, (peppers, carrots) try and stick to leafy greens (broccoli, kale, savoy cabbage, lettuce etc) and salad items (cucumber, celery)