From a first aid and CPR trainer, who is also fat.
The heimleich is scientifically as effective as slapping someone VERY hard on the back. The only reason it's so well taught is the man that invented it did a lot of great PR for himself. It's also a bit easier for smaller framed people to get the necessary force in, because people are often extremely scared to hurt people, even in life threatening situations.
With larger bodied people, whether they be fat, tall, muscular, etc. If you cannot get your arms around them, literally just slap the shit out of their shoulders. You want hard, open palmed slaps right in the center of the shoulders or slightly below.
If they are too tall for you to reach that high, guide them to lean over the back of a chair, and then slap slap slap slap slap.
It's been proven to be just as effective through many studies. It just doesn't have a trademarked name and a dramatic effect in film.
If you have to do CPR on a larger bodied person, again, fat, body builder, tall and broad, whoever, the trick to finding where you want to put your hands if going to be to take your hand and shove it in their armpit. No seriously. Put your hand in their armpit, then drag it in a straight line towards yourself until you're in the center of the chest, then put your other hand beneath that one. This is where you push. Then you are going to move the arm closest to you out of the way so you can get closer to them, and get the leverage you need to press down for compressions. The more of your body weight that is over your hands, the better the compression will be. Act like you are trying desperately to pack the last of your clothes in a suitcase, and just slam down hard on their chest.
They will make *horrible* noises. You might even break ribs.
But a broken rib is better than being dead.
One day, perhaps, other CPR and First Aid instructors will actually know and teach this shit. But the medical field is filled with people who don't know, don't care, or just outright hate fat people. So while this information won't fix your complaint, I do hope it helps someone out there with saving their loved ones, should it ever be needed.