Once upon a time I was looking for something similar - a lightweight yet fully functional HTTP server that I could easily embed and customize. I found two types of potential solutions:
So... I set out to write JLHTTP - The Java Lightweight HTTP Server.
You can embed it in any project as a single (if rather long) source file, or as a ~50K jar (~35K stripped) with no dependencies. It strives to be RFC-compliant and includes extensive documentation and many useful features while keeping bloat to a minimum.
Features include: virtual hosts, file serving from disk, mime type mappings via standard mime.types file, directory index generation, welcome files, support for all HTTP methods, conditional ETags and If-* header support, chunked transfer encoding, gzip/deflate compression, basic HTTPS (as provided by the JVM), partial content (download continuation), multipart/form-data handling for file uploads, multiple context handlers via API or annotations, parameter parsing (query string or x-www-form-urlencoded body), etc.
I hope others find it useful :-)