How do you shift your weight when leaning on a turn?
I think this relates quite nicely to motorbikes where you corner at very high speeds and I'll give a run-down of the techniques, why they are useful and how they apply, and how they might apply to cycling.

So when turning left:


You shift your weight over on the seat and tilt the bike left. This allows the centre of gravity to be slightly lower, aiding in stability and keeps the contact patch of the tyre to road more central.
Sticking your left knee out also. This is done for two reasons, firstly (if you're wearing knee protection) it can give an indication of when you're leant over too far (your knee touches the floor). Secondly it works like an air brake (for additional braking) and also will start pulling you towards the direction you are going slightly. You have to be going pretty fast for this to be effective, but it can help if you're racing.
I can't see any benefit of tilting the bike over whilst staying more upright. Higher centre of gravity, less control. It might be a sub-conscious impulse to not falling over low-side.


Another tip for cornering fast:


When going into a corner and you feel like you may run wide, or want to tuck into the apex a little more, turn the handlebars in the opposite direction to the turn (right) just a little. This is called 'counter-steering' and will cause the bike to tip over more and turn in a little harder. This can be a life saving technique if there is a car coming the other way or is overtaking you. Don't over do it though ;)


Also, ultimate safety tip: never brake and turn at the same time.

Source: I've been riding high performance motorcycles for about 5 years.