You can use Java with FastCGI. This is very flexible, but also a bit low-level for most Java programmers.
If you aren't afraid of servlets (they are only a very small part of Java EE!), I can recommend JAX-RS, it is quite easy to get started with. If you client-side is JavaScript based, you can avoid using JSP (which I would recommend you to avoid).
For example, see backbone-jax-cellar. The Java source is here. For a Java app, this is light-weight. He is rolling his own DAO, but that's the price you pay for using Java and SQL and no dependencies (other than JDBC). The code is reminiscent of object-oriented PHP if you ask me. The point is, that if you have a JavaScript client, you don't need template rendering or all that cruft and a REST interface should be enough.
If you are afraid of the heavy build systems too, I made an example REST Todo app backend (which uses an existing frontend) that only requires a POSIX system, the JDK and sqlite3, and gets its own other dependencies (including webserver). I did not use a DAO. The repository front page has a README.
Another possibility is the Play Framework which does not use Java EE. It is rather heavy-weight, though. Full featured though. You would definitely need to use an IDE for this, you don't need that for developing JAX-RS/FastCGI apps.