I'm on Jenny Craig and basically, I spend additional money on fruit, milk, salad, veggies,string cheese, Laughing Cow cheese squares, and maybe graham crackers. I'd say about $20-$25 additional per week. Also, if you decide to join JC, you can save money by not buying their "anytime" bars which are milk supplements. You can just drink milk You also do not have to buy their vitamans...tell them that you have your own.
For me, I spend less than I used to on food now that I am on JC. I know that JC is considered to be expensive, but I joined the Rewards program which gives me 10% off of food for the first 10 weeks, 20% off for weeks 11-20, and 30% off thereafter. My bill tends to be high because I only eat frozen lunches and dinner. The shelf foods are cheaper. Also, I eat a lot of cereal for breakfast so that's cheaper. You can make the program what you want.