To slight someone is to insult them, or to speak in a disrespectful or condescending way. It doesn't necessarily mean that you ignore the person. 'A slight' is an insult or perceived criticism.

I still see it used regularly. Here are three recent news items in England for your amusement. I have taken out the names. 1. She felt slighted when she found that she was not in the Queen's carriage at Ascot. 2. He felt slighted and was furious with Lady E.A. when she did not answer his phone call. 3. He felt slighted when he was not invited to be on the balcony.

"slight" as a verb is more about treating someone as if they are not important. It might be about ignoring someone, but it might also be about denying them something or actively not choosing them. It's deliberate. We don't often use that verb in modern spoken English, but you will find it in books and literature. You're more likely to hear "slight" as a noun in spoken English, meaning "a small amount" eg. "There's a slight chance we will miss our flight."