One of my friends is over 222 lb. He is a bit lazy to go to gym; so, I suggested he do stair climbing at home. He agreed to the idea at first but then told me it might be harmful given his weight. So is it okay for an obese person to do stair climbing?
To lose fat, you need to burn more calories than you consume. You can do this through eating fewer calories, burning more calories (i.e. more exercise), or some combination of the two. A combination of eating fewer calories and exercising more is what I (and probably most people in the health and fitness world) would recommend.
Your friend needs to address both of these. For the food part, there is a lot of information out there on this (everything from fad diets to getting the proper nutrients for your body). I could write a very long post on it, but since you asked only about the exercise I leave it at "he needs to eat less calories than he burns".
Now for the exercise part you asked about. Stair climbing at home can be a great place to start, even when overweight or obese. (As an extreme example, look at the TV show Biggest Loser. They have people over 400 and even 500 pounds do all kinds of intense exercises. I'm not advocating the extreme training they do on that show, but hope to make the point that even very overweight people can train if they are willing to push themselves.)
The thing your friend needs to watch out for is injury to things like the knees, ankles, and hips. If he is carrying around a bunch of excess body fat, impact to the joints over time can cause a lot of pain. As he loses the weight, it will be less pressure on those joints and movement will become easier. He just has to listen to his body and stop when it becomes painful (notice I used the word "painful" and not "uncomfortable" - "uncomfortable" usually means you are pushing yourself, which is good).
If he finds stair climbing to be painful, recommend something a little easier like walking. Go as far as he can one day, and then that distance plus a block the next. Keep adding distance and start to pick up the pace. Over time he can push that to a jog, then a faster jog, then a run. The key is to keep moving in whatever way his body will allow, no excuses.
I went from being overweight to fit in the basement of my house. All I had was a cheap pair of weights and an exercise video I got for free. At the time I could barely even do a pushup on my knees, and over time, with effort, I kept pushing until I was doing one handed pushups and a variety of crazy exercises. Your friend can do it too, if he stays motivated.