Will the box tip when a drawer is opened?

This will only be a problem when the top box in a stack is pulled open more than halfway, so the center of gravity is past the front edge of the box beneath it. All lower boxes will be stable when pulled out, even if they are extended to their full length (See above). The tipping issue is a minor problem and is easily corrected a number of ways. The simplest solution is to place another box such as a long box on top of the stack to act as a counterweight. Another solution is to attach a trim board like a chair rail to the wall on top of the back edge of the top box. Another solution, particularly if your DrawerBoxes are stored in a closet, is to install a shelf on top of the back of the top box. This will provide you with additional storage as well as keeping the top box stable when fully extended.