I cant find even 1 website that clearly explains how excess insulin can cause weight gain. If I'm on a ketogenic diet & drinking Diet Coke, which raises insulin levels in blood, how would this possibly lead to weight gain if I'm not eating carbs????

Body makes carbs. Body can make carbs from protein and fat. Insulin facilitates entry of glucose into cells where the glucose turns into fat. To avoid weight gain, you need to reduce total caloric intake. Insulin is a growth factor. By doing so-called ketognic diet and diet coke you are not doing your health any favors.
Wish you good health! - Have a diet rich in fresh vegetables, fruits, whole grains, milk and milk products, nuts, beans, legumes, lentils and small amounts of lean meats. Avoid saturated fats. Drink enough water daily, so that your urine is mostly colorless. Exercise at least 150 minutes/week and increase the intensity of exercise gradually. Do not use tobacco, alcohol, weed or street drugs in any form.
Practice safe sex, if you have sex.
Get HPV vaccine.