Yes! I think it's doable, if you build up to it gradually over time. You are only in your third week of exercise, so it will take some time to build the endurance you will need. I'd suggest starting off with a smaller, short-term goal like a 5K. Then work up to a 10K, then a half-marathon,and so on. There are lots of beginner training schedules out there to show you how to train up to races of varying lengths. Running the shorter races will give you targets to shoot for, help you in your training, and give you some experience with running "events".
When you are first starting out, it is most important to establish a consistent running routine. If you try to push too far, too fast --that can be a recipe for injury. Take it gradually and don't forget the cross-training. Strength conditioning, core conditioning and stretching are also important for overall fitness and injury prevention.
But, yes, I believe that anyone in reasonably good health CAN complete a marathon given sufficient time and conditioning and motivation. It's a wonderful goal and a tremendous feeling of accomplishment when you reach that goal. And the training between now and then should help you toward your weight loss goal as well. I wasn't considered overweight when I started running, but I've seen lots of people out there that were ... and they could do it!