"shall we go excersize together?" "Do you fancy a run or to go swimming" Do activities with them and cook them healthy food while egging them on how much weight their loosing and making them feel good/attractive.
my mother went vegetarian because she thought it would get us eating better. it pretty much just added more bread and cookies to our diets; how's that irony for you?
but seriously, I agree with ~kissofthevampire364 ; working out together is really good for motivation, and eating healthfully is better when the entire family (in your case, it might just be you two, i don't know.). just don't say something insensitive, like "you need to go to the gym, here, i'll go with you." include yourself in the conversation, regardless of how fit you are. approach it as a group effort and you should be fine
I think that you shouldn't approach it in like the "need to loose weight" way, but more the "need to be healthier way". Like... if that person is eating a lot, you should be like... that isn't healthy... or something... and start suggesting healthier ways to eat. that way i think you would appear more caring rather than offensive
First you start taring the scale back and loosening the waist on their trousers (or swapping out the labels - either way, you'll need to know a bit of sewing. It's a slow process, but they'll start to believe they're losing weight.
Then one day, suddenly, you reset the scale and put the waist/labels on their trousers back to default. They'll be all "wtf?! why?!" and you'll be all "I think it's time we had a talk."