If you slight someone, you deliberately ignore her, or treat her with indifference. If your best friend walks past you in the hall without so much of a word, she has slighted you.
All the meanings of Slight stem 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, slight means to ignore or be indifferent toward someone; it's also the noun for the act of ignoring. If you directed a movie and the starlet doesn't thank you in her award acceptance speech, you'll be offended at the slight.