It doesn't infuriate me, but I can understand being concerned about having family members who eat unhealthy. My dad and younger brother both always eat complete junk and my brother is a gamer who almost never gets any physical activity. I actually now weigh less than my brother which breaks my heart because I am still so far from healthy. My dad already has diabetes that keeps getting worse because he eats horrible stuff and a ton of sugar. I have heart problems that require a low sodium diet and I'm trying to lose weight so I'm eating healthy foods, but I'm living at home right now to save money. I try to suggest healthy foods but my dad fights me all the way even knowing that because of my health problems I need to eat healthier food. So it usually ends up that my family has one thing and I just eat raw fruits and veggies. My mom has tried to make changes like extra-lean meat, and I have my own skim milk and wheat bread, but my dad even refuses to switch to whole wheat pasta. I want them to eat better because I care about their health, but I know I can't make them change. I'm very careful with my brother about his weight because I know what it was like having people make comments to me. I'm just trying to be his big sister and hoping that he'll see me being healthier and come to me for help. I keep asking him to come play catch with me or go lift weights, so far he has turned me down but I'm hopeful that I'll eventually get a yes.
I think you should be careful with your brother that you don't make him angry with you or hurt because that will just make him turn away from your help. All you can do is be a good sister. Invite him to do things he would have fun doing that would get him moving (bowling, swimming, playing a sport, etc). If you find a healthy food that you really like that you might think he'll like too, try something like "Hey, Bro, try this. It's good stuff." I've got my brother to start drinking diet berry green tea instead of Mountain Dew by doing that. Small changes will help. Just make sure that everything you do, you do in complete love.