PunyMVC is probably the most lightweight PHP MVC framework.
It barely has any features at all. In spite of that, it's
very useful for writing web apps, as it helps you keep your
code organized in a logical way, but the framework itself
never gets in your way. At all. Plus, there's really no
learning curve (assuming you already understand the MVC
paradigm and know how to code in object oriented PHP).

The file public_html/index.php is really the entire framework.
But a very, very simple blog demo app is included as well, to
make it easier for you to see how to organize your code.

Because most MVC frameworks (and web apps in general) use a
relational database like MySQL, I decided to use MongoDB in
the demo. The demo data is located in the included dump/
directory. To use it, simply install MongoDB on your system,
and use "mongorestore" to create the punymvc_demo database.

Once you've loaded the data, all you need to do is move the
contents of public_html (including the .htaccess file) into
a web directory somewhere, and then access it through a
browser. You can view a detailed walkthrough of setting up
this demo app here:

http://dave.ag/an-mvc-framework-in-799-bytes/