What signs does exagerating jokes on you send?

First, it shows that you are approachable and don’t take yourself too seriously.
To take a joke like that and turn it into another joke shows a sense of humor, and is someone that makes people comfortable. They can say what they want around you without having to be too careful.

Second, it shows that you are secure.
To dig yourself a deeper hole, so to speak, shows that you don’t care about what people think. You can roll with jokes, and don’t mind being the occasional butt of jokes. You know it’s all in good fun, and you want to extend the fun.

Finally, it establishes you as having wit and clever banter.
When you have a guideline that you can follow (exaggerate to the 10 th degree), it becomes too easy to think of something clever to say, and people will take notice soon