OpenWebBeans 2.X.X has a dependency you could include to make it work in Tomcat (“openwebbeans-tomcat7”).
How do I make OpenWebBeans 4.0.X work in Tomcat?

It logs that it has added beans archives, but no injection actually works.
All fields Attributed with “@Inject” are equal zero.

OpenWebBeans 4.0.X has zero documentation so I cant figure this out on my own.