Especially if they are unhealthy people who eat unhealthy meats

Heavy meat-eating could be part of an overall unhealthy diet or unhealthy lifestyle

Yes, and therein likely lies the key. As we pointed out before, comparsions mean little if the meat eating group has people who live an unhealthy lifestyle and eat unhealthy processed meats and meats from animals subject to growth hormones and antibiotics.  As a whole, people who eat less meat tend to be more health conscious and active.

I hate to see these studies that don't take into account the types of meat eaten and the overall lifestyles of the meat-eating group, and end up giving the wrong impression that meat eating in and of itself is unhealthy - which is no more valid than it is to say that eating vegetables is healthy in and of itself.  That is about as valid as it would be to take a group of sedentary people who ate mostly GMO vegetables grown in depleted soils and comparing them to people who ate healthy meat and were active and health conscious.  As is true for vegans, the source of the food is key, as is the overall diet and lifestyle.

What do you suppose a study might show which looked at people who ate only healthy organic free range type meats and were as active and health conscious as a group of mostly vegan people would be?  Perhaps not only less weight gain, but actual weight loss.  Eating only or mostly healthy meats might itself cut down meat consumption - as Griz has pointed out, when you eat healthier meats as a part of an overall healthy diet and lifestyle, meat consumption tends to come down anyway.

By all means, promote the health benefits of consuming goodly amounts of healthy vegetables, fruits, seeds, nuts, legumes, etc.  But don't make meat itself the culprit.  Instead make what humans have done to meat, the same as what they have done to our vegetables, the real culprit.