I am using vb version. I feel quite strange that all the business layer delete method is not shared function, it means that we need to instanstiate an object before we use the delete method,
as instantiate an object in this project will in turn get the relevant objects details from the data layer and this step seems like redundant..
What is the reason not write it in shared function, that pass in the primary key of the table as argument?

For a simple function like Delete you can make it into a shared
(static in C#) function if you want.

Instance methods are helpful when you need to maintain state between several calls to an object.

It's not "right" or "wrong" to use an instance method in cases where you don't need to save state between multiple calls (like in this case). Some people prefer to use instance methods to make the code more consistant.

Shared (static) methods are more efficient at the CLR level, but that difference is slight when you consider the time it takes to hit the database.

Eric