Thanks for bringing your question to JustAnswer.
Yes, Cymbalta does have weight gain as a listed side effect. The two antidepressants that don't seem to cause most people to gain weight are Prozac (sometimes even causes weight loss) and Wellbutrin. You might want to consider asking your MD to switch you to one of these. (If you are using Cymbalta for pain relief, note that Prozac and Wellbutrin don't have pain relief effects.)
30 mg of Cymbalta is the typical starting dose, so he will start you on the appropriate starting dose of the new medication. Here are articles that explain the dosages typically used: