This is my own experience with social barriers to stereotypically healthy behaviors like exercise and eating “healthy” foods. (I say “stereotypically”, because there are a lot of other things that are important for health that we don’t associate with fat and don’t assign a lot of moral value to. Because of this, they tend to be less fraught for fat people.)
There are significant social barriers that make it harder for fat people to exercise, and they usually are worse for larger fatties. Through some combination of relative thin privilege, regional differences, and luck, I’ve never been directly fat-shamed while exercising. I do feel self-conscious and out of place when I’m the largest person at an exercise class, which happens surprisingly often considering that I’m a small fatty/inbetweenie. I’m usually the largest person in classes with less than 10 people. The same feeling of being out of place also happens if I’m in a gym full of skinny people. I also often think I detect a certain amount of condescension from fitness instructors or people to whom I mention exercising. But as I said, I’ve been lucky. I haven’t been turned away from classes, mooed at while out running, had much trouble finding sportswear (I do have to order most stuff online), or been in a class where I couldn’t do the exercises without modification because it was designed for smaller bodies that took up less space.
For some posts by people who have been fat-shamed while exercising, see here, here, here, here, here, and here. (I didn’t find as many of these as I thought I would; I’m pretty sure I’ve read some good examples that I wasn’t able to find again. If anyone would like to suggest a link in this category, put it in comments. Or share your story in comments if you have one.) For examples of someone trying to be complimentary, see here and here. Sometimes you can get comments just from trying to read about exercise.
For other health behaviors, whether the social pressure leads to more healthy or more unhealthy behaviors is less clear-cut. A fat person eating a sundae will probably feel more self-conscious about it than a thin person eating a sundae. But they may also feel like a poser if they go buy kale at a farmer’s market. And they may feel almost as self-conscious with “healthy” eating habits as with “unhealthy” eating habits, because people may start in with “Good for you!”, etc., thinking they’re on a diet. I haven’t had any comments that were quite so obvious–I haven’t had that many comments on what I’m eating, positive or negative–but I actually feel more self-conscious ordering a salad at a restaurant than a regular entree.
Which brings me to another problem: even if you’re trying to give someone encouragement for healthy behaviors rather than shame them for unhealthy behaviors, it can cause them to be more self-conscious and end up being discouraging. It can also come across as condescending. Especially if they feel like they’re being singled out because of their weight.