If your friend is fat and overweight, you need to do more as a friend than simply giving them unconditional love. There’s nothing wrong with individuals who struggle with weight issues, but they are overly sensitive about discussing their weight and yes they know they are big without you mentioning it or having obesity as the centerpiece of your friendship.
However, you can be clear to them that you care a lot about them by committing to going to the gym together and working out. Also, cut back on the alcohol and eating out because you care for their health.
Be a friend, but don’t ever nag your overweight friends like a parent. Otherwise, they would rather be friends with a gerbil instead.