Breakable MVC framework written in PHP
Nice initiative on a lightweight MVC framework!

Note wanted to add more reference links, but it won't allow me to do more thanb 2

Config


Pass the default controller setting to the function 


or 


Pass all routing related settings to the __constructor. and use them as class attributes


Loader class

The setup isn't all that bad. Nice and lightweight. A few things, i would do different;


Seperations of conserns (One of the SOLID principles). Let the loader just load an return the instances.

Don't bind the loaded elements directly to controller in you class, so in future you could also use it for different cases then just the controller class.
Don't render the views in a loader. Make a render class or such. If you way of rendering changes, you would have to change the loader. Which ultimately don't make sense.

Make APP_PATH and LIBRARY settable within the loader, and call them differently


A loader class attribute for each load path 
Default the attributes to APP_PATH and LIBRARY
Getter and Setter for load paths
Now you would be able to integrate different paths / modules etc. Making it more flexible

Autoloader for library classes


By registering the loader as php autoloader you can just instantiate a class. 
If not yet loaded into mem, it will be sent to the autoloader. 
There you resolve the path it should be on and instantiate.



Security

The big thing in this form of autoloading is the concern for input. Make sure all input is either given by the application itself or validate it.


Validate user strings that will be autoloaded (eg. controller names)
You can do this by first doing a realpath() check on the computed path. And make sure the realpath() is within the locations you would expect.
This prevenst users from entering stuff like '......\uploads\mayhackscript' which would be executed otherwise.


This is a real danger.

General remarks

Take a look at te following;


SOLID principles
PSR-2 coding standards; note, it extends PSR-1 which extends PSR-0


Good luck on your project!