Sad to see any 18 year old depressed, but you have to understand why before you can help her. You mention overwieght, and lazy stay at home, and they all go together, so you already know the problem, it starts with low self esteem due to being overwieght. Obviously, if she is beautiful, then it is all about the weight, and this can be easier to change than your looks.
You have to address the overweight issue first and foremost for being a recluse at 18 is not a good sign, nor is falling into a lazy lifestyle. When I was 18 I couldn't be stopped, I was always on the go, as are most 18 year olds.
Find a gym which has young overweight classes, it is the only way, you have to align with others in the same situation, who are overweight and want to make a change in their lives. You can't do this when going to a hardbody gym, so look for special overweight classes and make some friends for ongoing support.
Excersise is never easy to get started with, but it is the only way. Obviously, you have to pay attention to what you are eating, so enlist a nutritionalist to set up a healthy diet plan. It will take a commitment, but doing nothing is not the answer for it will only get worse the older you get. I got motivated by watching the TV show where as a group, people lost thousands of pounds, get inspiration through others. Most who were on the show would be glad to offer support for they were all in the same overweight boat, and it was sinking fast.
Good luck, Child-Shield-USA.com