Runners wanting to lose weight should eat a combination of complex carbohydrates, lean protein, and healthy fats from a variety of whole or minimally processed foods like fruit, vegetables, fatty fish, eggs, poultry, tofu, beans/legumes, and whole grains. These foods support both weight loss and athletic performance.
Modest weight loss achieved through exercise most likely won’t affect a runner’s overall performance so long as there is adequate intake of calories (particularly from carbs and protein), and pre- and post-run nutrition are prioritized.