Hi Jeremy! I think we are mostly on the same page but my perspective is shaped by my own negative experiences with being "complimented" or inspected by others. I'm hyper-sensitive because of my own experience of having my mom and aunties constantly commenting on my weight when I was a teen (e.g., "Oh, you've lost some weight, you look great!" but then a month later, "Oh, you've put on some weight, you should watch what you're eating!"). I was an athlete and ate when I was hungry, so I never deliberately dieted to lose weight but it did yo-yo a bit. It was never enough that I noticed it (2-5 pounds?), but apparently eagle-eyed older women noticed it.
Even now, unless someone said to me, "Anna, I've been working hard to lose weight," and prompted me to respond to that, I don't think I'd volunteer a compliment/observation about their weight.
I actually don't comment about someone having nice eyes or a great smile. It may be because adults used to criticize my eye shape (I have monolids, so particularly small eyes) and they would say things to my face like, "You'd be so pretty if you only got eyelid surgery." And yes, teachers always commented that I had a nice smile as I'm a cheerful person, but I felt my smile was a genetic lottery ticket (I never got braces). So I assume it might be more meaningful if I complimented someone on something they did, rather than something they were born with.
I particularly take that to heart when talking with kids. Too often, adults tell girls, "You have such pretty eyes/hair/smile." I prefer to comment on something they chose (e.g., cool striped socks, a book or toy that they're holding, etc.). Not sure that's the best strategy, but it makes me feel like I'm not making them feel like I felt as a child being "inspected" by the adults.