It fails with Weld 3.0.0, 3.0.1, and 3.0.2.
I'll try again with Weld 2.x as I don't remember exactly which version I used previously.

The environment is Java SE + Jersey + Grizzly.
The class with the private observer is application scoped.

According to my logs, the following sequence occurs:

• First, an application scoped class has an observer to observe the application scoped context initialization event:

  @Observes @Initialized(ApplicationScoped.class)

• This observer is also an intercepted method; it's private and it's successfully invoked.
• During the execution of this observer, an event is fired.
• This event triggers the instantiation of another application scoped class, which has a private observer for this event.
• An exception occurs when trying to invoke this private observer.