Which AS/Weld version? There was a lot of trouble with the JNDI names at one point. In Servlet envs it places it in the SC for quicker lookup. I think there is also an EG proposal for standardization of this.
Specification-Title: Weld Servlet module
This is the default one in the Maven archetype, I've tested with latest TC6 and GF3, none of them working, so should I use JNDI or ServletContext lookup?
In Tomcat, you need to follow the the reference guide to set up JNDI binding for the BeanManager. You then need to access it at java:comp/env/BeanManager not java:comp/BeanManager - Tomcat doesn't allow you to bind outside of the java:comp/env space :-(
For GlassFish, you should discuss on the GlassFish forum.
Have you tried using JBoss AS - we can help you with that one ;-)
In case anybody has the same question, here is the jndi name in different containers:
GlassFish3.0.1 and JBoss6.0M4: "java:comp/BeanManager"