I agree that a lot of people don't recognize there is a slightly negative connotation to the word "skinny." But by the same token, I have to say, if someone ever used that term to describe me (as in, "you've gotten skinny" or "skinny minny") I would take it as a compliment. Any word that implied I was thin would be welcome! However, I can also see how in other situations said to other folks, it may not be used as or perceived as a compliment.
People do make out-of-line comments about weight all the time. I remember a (very thin) colleague at my former school remarking to another woman (intending to compliment) that the woman had lost "a ton of weight" and that she "should never let herself get that way again." What is wrong with just saying, "You look great!" or "You've lost some weight" rather than saying a "ton" of weight.
The other thing that hasn't been mentioned...I have a very fit acquaintance (I'm talking she has very little body fat, 6-pack abs, size 4-6) who constantly talks about how she's getting fat or she looks fat, etc. I wonder if it ever occurred to her to think about the people around her who are bigger than her. Personally, I think she does it to fish for compliments and to deliberately make others feel bad.