Implementation of Javascript Classes and Inheritance
I read your code several times, and I could only find few observations:


jQuery has extend as well, the idea of it is sound, you could consider working with arguments and allow for n objects like jQuery does
I am not sure that always overriding the constructor is a good idea in extend
In the same vein, your approach does not allow for custom constructors that take parameters, whereas most OO classes have those ( new Customer( "Bob" ) to give a silly example)
From a lint perspective:

You declare var key thrice in extend, you only need to declare it once, preferably on top
for loop blocks do not need semicolons
You should really look into .hasOwnProperty(), I am pretty sure your code can cause subtle bugs by smushing everything together