What kind of messed up logic is this? Of course you should be concerned about the health of your friends and loved ones. If I have a parent who is dying of cancer I'm not just going to ignore and decide "well that's between them and the doctor." If my best friend decides to start smoking four packs of cigarettes a day I'm going to tell them to cut it out before they kill themselves. Why? Because that's what friends do. They look out for you even if you don't want to look out for yourself.
Maybe talk to them about their health and medical aspects of their lifestyle as opposed to telling them to lose weight. This can lead to weight obsession and eating disorders, while keeping it purely medical helps more :)
Also, how do you know they're fat/overweight? What if a girl is perfectly healthy and wears a size medium but her boyfriend is just an asshole and constantly tells her she's obese and needs to lose weight? That's not being a concerned for someone's weight, that's being an asshole abusive boyfriend. Hell, I was friends with a girl a couple of years ago who was super tall and wore a size small and her boyfriend still constantly told her she was fat so much that she ended up being anorexic because of it and had to be hospitalized. The point is, it's not someone else's business to tell you what to do with your weight. Yes, being overweight is not healthy, but you don't have to be an asshole about it.
All are valid, but at the end of the day any friend or lover should be honest. Lying and BSing get us nowhere. I helped my wife lose weight, but she knows full well I loved her before and will love her even if she gains it back. She knew this, and let me help. Why? Because that could be more time we spend together down the road when we're senile. It could be because I love her, and care, and now she's thinner and thinks she's hot as hell. Boosting self esteem? Check that off our list. Let's be real and help each other at the same time guys. It's not about hurting, it's about caring.
When I was a freshman in HS, this guy told me he was into me but didn't like chubby girls. So, I used this as motivation to lose weight. I was happier, and I realized that he's a dick and I had nothing to ironically lose when I lost weight, but I was happier. You shoulda seen his face our Senior year when I bumped into him in the hallway.
Sorry fat is not beautiful, and this is coming from a fat guy.