Sarcasm is usually a real feeling wearing a costume. Look under the joke.

A joke is a safe way to say something true. The costume gives the speaker an exit, so if it lands badly they can say they were kidding, and that escape route is exactly why humor gets used for the things that are hardest to say plainly. The feeling underneath is generally sincere.

When a comment stings or keeps repeating, take the content seriously even though it came wrapped. Ask about it gently and without accusing them of hiding. And notice your own jokes too, especially the ones you keep making about the same person or the same subject.