1. The "You've clearly lost weight but I don't want to imply anything" method.
INT. PARTY OF SOME VARIETY - DAY
A relative and/or friend who hasn't seen you in a while keeps staring at you from across the room. Eventually, you cross paths. You juggle your mimosa as he/she smiles in an oddly conflicted fashion.
RELATIVE AND/OR FRIEND
You know, you look great.
You look down at your outfit, now sporting a dark stain and smelling faintly of spilled mimosa.
Um, thanks. So do you.
You wait, thinking that, perhaps this conversation might continue. It does not.
RELATIVE AND/OR FRIEND
You saw Frozen, right?
The general idea behind this seems to be that your friend and/or relative has noticed that you have lost weight. Maybe they've watched you struggle with it for a while, or maybe they simply haven't seen you in a year. Either way, they would really like to compliment you on your appearance, but are entirely unsure if making the compliment weight-related is appropriate. The expectation is that you will have the same logic as a girlfriend in a male-centric sitcom; they'll say "You've lost weight, congrats." and your response will inevitably be "What? Did you think I was fat before? Did you think I needed to lose weight? Did you forget our anniversary? I think we need to see other people."
2. The "I think there's something different about you, but I can't quite figure out what" method.
INT. OFFICE - DAY
Your professor who hasn't seen you since you were in a terrible place in your life looks you over. She smiles.
You look like you're doing well.
Thanks. I feel like it.
Yeah, you look...healthy?
So, did you see Frozen?
This one's filled with nuance. With my weight loss, it wasn't so much a weight loss as a return to form. I'm naturally plus sized so, with some people, it's often hard for them to tell when my weigh fluctuates. People assume that losing weight takes you from fat to skinny with nowhere in between. With me, it's less "I was fat but now I'm skinny" and more "I'm a bit more balanced and comfortable." I had gained a lot of weight during a particularly bad stint with depression, and since getting that more under control, I've lost quite a bit of what I've gained. The result is that I seem different. I'm happier, a bit more confident, and wearing pants that fit me. Because a surprising amount of weight loss is actually internal, when people pick up on it, they're sometimes not picking up on the size of your girth, but on the way you present yourself. As bizarre as the phenomenon is, it's admittedly pretty amusing to watch people stand around desperately looking for the right words to describe you.
3. The "throw caution to the wind" method.
INT. FUNERAL HOME - AFTERNOON
You've just arrived home after a six-month stay in another country. You immediately find yourself at a funeral, where your grandfather spots you.
Who are you?!
He laughs. Despite having heard the joke before, you laugh as well.
I was wondering if I'd ever see you again.
He takes a moment to look you over. He seems proud.
Did you lose weight?
As a matter of fact, I did.
You look good, kid.
Did you see that movie everyone's talking about? Freeze or something?
I like this option best, but it is, admittedly a risky one. Weight's a pretty tricky thing to discuss. It carries a lot of...well, weight. We're conditioned to think about it constantly - whether it's "Hooray! You're skinny" or "Damn, you're fat!" or "Whatever you are, you need to do something about it." The compliment of "Hey, have you lost weight?" instantly brings this to light. On TV it's seen as the thing you should always ask a women, whether she wants to lose weight or not. Because of this, it's lost some of it's legitimacy. It's a shallow thing to say, rather than a genuine one. It's left us constantly looking for the correct thing, and never really finding it.
Personally, as a sufferer of thyroid disease, as someone who has struggled with weight and self image through most of their life, I'd say compliment what seems to be on the forefront of the person's mind. It's not easy, you may have to become a psychic. But for a lot of people, I know that "It seems like you're doing a lot better than you were before" would mean a lot more than "Hey, you're a weight I can name, but still can only barely find pants for!"