Shifting your weight alters the lean angle. You get off the bike on the inside so that the bike remains more upright. If you remain in line with the bike then the bike must lean more.
Lean angle is calculated based on the combined Center of gravity for you and the bike.
Also, rake/trail doesn't affect lean angle required to make a turn, it determines effort required to change the direction of the bike in order to achieved the desired lean.
I missed this.
Yes it does btw I will give you an example.
We will use an extended swingarm in this example since its somewhat common, most of us hate them, and we all know what they are.
The first thing adding something larger to a bike does is add weight. This alone doesn't really matter, what does matter is where that weight is added. If the weight is added below the center of gravity it will lower it and vice versa if higher. We know that a lower "CoG" requires less lean angle. A change in ride height would do the same.
The negative side effects of a swingarm like that greatly outweigh any gains by slightly lowering the CoG however (if it even does).
The back tire acts as the pivot point. The tires are now farther apart then they where. This means the front tire will have to travel farther to make the same degree of change in direction as before. This means the bike will turn slower. In order to take a turn at the same speed as a bike with a stock swing arm, the front tire will have to be moving faster in regard to the lateral correlation to the back tire. This means the bike will have to rotate faster on its Y axis to make the same turn at the same speed.
Rotating faster on the Y axis equals turning faster at least as far as inertia is concerned. The bike will have to lean more to compensate and maintain the turn in question with the same forward speed as the other bike. Hence rake and trail or suspension in general effecting the required lean angle of the bike.