For a weekend, all things considered, you'll probably save a bit of weight by not cooking. But you'll also probably be surprised how little weight you'd save.
As has been pointed out, an esbit stove and adequate fuel and small cookpot only weight a few ounces. Assuming your food weight for no-cook food menu is equal to the cooked food menu you'll probably end up in about the same place.
But it can get tricky. For some no-cook food (tabouli, some no-cook oats) a lot of sitting time can be required. If you are on the move you'll need to have a secure container to keep the soaking food in. A ziploc might work, and might also produce a spectacular mess instead of supper.
One of the things to be really careful about is that food-value-to-weight ratios tend to matter a lot more than the weight of cooking equipment. It is really easy to construct a no-cook diet that involves carrying more weight per day than a plausible diet with a cooked dinner and cold cereal for breakfast.
I do some no-cook meals, usually tabouli or sometimes just have a big sandwich for dinner the first night out. In general, I don't see a big advantage (or disadvantage) to not cooking. It is more about psychology. Having a warm bowl of chow at the end of a long, rainy day, may not have any physiological benefit at all, but it can have enormous psychological benefit. Coffee and tea have no real food value but can have an enormous impact on your morale.
Remember, this is about having fun. Just do what is fun for you.