I wish to embed a very light HTTP server in my Java Swing app which just accepts requests, performs some actions, and returns the results.
Is there a very light Java
You said "very light" twice, so I think JLHTTP might be a good match for you. You can embed it as a single source file or a ~35K/50K jar file, yet it supports most functionality you'd need in an HTTP server out of the box.
Disclaimer: I'm the author. But check it out for yourself and see what you think :-)