Anything slight is very small. There's a slight chance you'll run into a celebrity in New York City — in other words, don't count on it. A slight is also an insult, like giving someone the cold shoulder. Burr.
Every meaning of slight stems from the Old Norse for "small or flimsy." If you have a slight build, you're slim with small bones. A slight deviation from your plan is a tiny adjustment. As a verb, to slight means to ignore or be indifferent toward someone; it's also the noun for the act of ignoring. If you direct a movie and the star doesn't thank you in her award acceptance speech, you'll be offended at the slight.