Can stopping insulin make you gain weight?

No. One common side effect for Insulin is weight gain. Stopping Insulin should not cause weight gain. However, if your blood sugar is out of control off of insulin, the fluid shift can transiently cause weight fluctuation. Don't stop Insulin on your own. Talk to your physician first.
Do not do it. Stopping Insulin is never a good idea unless it is under a doctor's supervision. The one possible result will be uncontrolled diabetes which can pose a serious threat to your health and life.