Consider that even if she adhered to your only eating in the kitchen rule in your house, it would not be the solution to her weight problem. You make good points about healthy eating habits, but being overweight is a complex problem, with multiple solutions and strategies that almost always need to be applied together to achieve success. This ONE particular rule isn't the battle you want to pick to enforce with her. It's having a negative effect on your relationship. It's not helpful, and it's not worth it to dig in your heels here.
She's an adult, free to go out and eat whatever and whenever she wants to eat. Heck, even teenagers have so much freedom just to eat whatever junk food they desire, out of the house. My 16 year old came home with Arbys fries and shake tonight. She and her friends went there after school. She used her babysitting money to treat herself. Sometimes it takes awhile before young people realize and regret that too much indulgence packs on the pounds. And only when they get to that point of discovery, they find the motivation to change some unhealthy habits.
What can you do? Don't buy her junk food, which I believe you don't so that's good. Stock your house with healthy foods only. Eat meals together as a family. She probably won't participate in much of that (my 18 year old doesn't). But still always invite her to join you at the kitchen table for meals.
Start an exercise program. Invite her to join you. Yoga classes or videos, bicycle riding, whatever. If she declines, do it anyway yourself. You'll be a good role model. And she may decide to join you down the road if you keep inviting her. Not by shaming her, but by welcoming her company.
You seem to resent paying for the costs in general for obesity in society. That's a big issue, for sure. But don't take it all out on your daughter. At 22, she would probably really desire to be living independently. Consider encouraging her in pursuits that support her independence, school, work, etc. It will help bolster her self-esteem, and with healthier self esteem, she may start taking better care of herself.
And finally, I will say that your daughter is the only one who can decide and find the motivation to lose her extra weight. Accept that it is her responsibility and choice to change, not yours. Maybe she's just not ready yet.