Prozac can cause weight gain around 10 pounds in about 25% of people who take it. This occurs with longer term use, usually about 6 months or more. Some of the other anti depressants also cause weight gain, including tricyclics such as Elavil and Trofranil.
There are a number of theories as to why Prozac and other anti depressants can cause weight gain. Some feel it is because people regain their appetites after being depressed (and therefore not eating) before taking the medication. Another theory is that the medication causes a change in metabolism. The person feels the need to eat all the time. People who have taken anti depressants also report feeling intense carbohydrate cravings which are hard to control.
There are other antidepressants you can take to lessen the chances you will gain weight. Serzone and Effexor both usually do not cause weight gain. And the drug Wellbutrin can even cause weight loss in some people. Trying another class of drug can also help. You just have to be careful to find a drug that will help alleviate your symptoms while balancing any negative side effects. That is why it is common for people who use medication to try many different types of drugs before they find one that works for them.
I hope this has helped,