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I would think how fast you go is an individual choice. Some people might not be able to run any faster than someone else's fast walk. If you feel like you're running too slow, and you have the physical ability to go faster, then I would say go faster. If you're going as fast as you can already, but it seems like a fast walk, then you're doing the best you can and that's just fine.

If your runs are too easy within a specific program, then I suggest you change up the program or change to a different week within the program that is more intense. It sounds like you are also trying to focus on losing weight. Dieting should be what you concentrate on while trying to lose weight (which sounds like you are doing) and sticking to a program that isn't too intense might be a good option for you to focus on what you are eating and your diet. Cutting out a calories from your diet, while also trying to get more intense workouts/running in, might be too much for your body. Give it time and find out what works well for you.