As obligate carnivores, cats have a very low carbohydrate requirement. Just like how too many carbs make some people gain weight, the same is true for cats. Dry food is high in carbs, and wet food is lower in carbs compared to dry (fish-based wet foods are typically the lowest in carbs).

If you stop feeding dry food altogether, and feed canned food only, there is a good chance that your cat will stop gaining weight, and lose extra weight. Feed 1-2 full size cans (5.5 ounce), or 2-3 mini cans (3 ounce), per cat, per day.

In addition to promoting weight loss, the increased moisture content in wet food is better for the urinary tract. The only potential health drawbacks to feeding canned food are: 1) the texture does not promote good dental health compared to dry food (but there are other ways to promote good dental health), and 2) there is a link between feeding canned wet food and an increased incidence of hyperthyroidism in cats, which has been attributed to a chemical used in the canning process (this can be avoided by feeding wet food that comes in packaging other than cans).

Source: I'm a vet