CodeIgniter, which is what the author recommends and I have used extensively, is already a very lightweight framework, or at least compared to some of the very opinionated ones like Zend. CI goes out of its way to make sure you can use or ignore as much of the framework as you want, with the exception of its core controller and routes system.
Components like templating, views, active record, form validation, etc, are completely optional, and it's trivial to replace or extend components without having to mess around with any of the core code. Just don't load that component, and use something else instead.