Both recycling facilities and trash facilities do this, and it would probably be a cool (if not exactly novel) project to take on.
There are many ways to separate materials in bulk. The method you are referring to is similar in theory to using size to separate waste using a large rotating trommel. I don't know about separating by weight, but perhaps density.
The problem is that some materials that you would want to classify together disply characteristics of different materials. For example, if you want to get rid of steel in your feed, you might run the material on a conveyor under a powerful electromagnet which would pull much of the steel out of the stream (there are, of course, inefficiencies, and sometimes small pieces of steel get stuck under larger pieces of, say, plastic refuse). However, you would likely want your aluminum products to go to the same area of your plant that the steel does, since they are metals and will go through similar recylcling processes (as opposed to plastics), but the Al won't be picked up by the magnet, so you've got to find another way to separate.
The number of separation processes (and the number of times the feed must pass through each for optimal recovery) will be determined by just how varied you want you recycling to be. If you simply want to sort between steel and aluminum recycling, then you've got a fairly easy job. However, if you want a process which will separate steel, Al, cardboard, plastic, and be able to separate paper products from things like plastic wrappers), you'll have a much more complicated system.
It's a good idea. You might have some trouble finding ways to make it a novel approach to this issue, but there are so many ways to separate refuse that you'll have a decent amount of leeway as far as ingenuity is concerned.