Hi EV,
Great questions. First, I think it's important that you continue to get those cardio sessions in. Considering your goal is to lose weight, they are critical to the process. You are absolutely correct in that your muscles need time to repair and grow. However, based on the description you provided, since you are doing just one circuit, the cardio you are doing afterwards is not going to counteract your work. The machines show you the muscles working to perform the exercise, but keep in mind that your muscles are not working in the same capacity and with the same intensity that they must in order to lift weights. Also, if you were really sore and completing the cardio put extra stress on your muscles, that would be different, but it doesn't sound like that is the case.
My recommendation is that you try to up your workout to two to three circuits. Make sure you are lifting with intensity. Keep up the cardio, but smartly. If you just lifted legs one day and are sore the next, don't overdo a form of cardio that uses the legs too much. On those days, try the rowing machine, yoga or upper body ergometer, for example. Exercises like walking and the recumbant bike aren't going to place to much extra stress on the legs unless you use a lot of resistance or a steep incline. These are the kinds of adjustments you can make when you need to.
Keep up the great work.
Good Luck,
Paul