Take a look at J2EE 6 - you might find it's Spring which is the heavyweight these days. Although as of 3.1 at least the need to write your programs in XML is going away...
I'd argue that the right time to start writing Java EE applications is right now. With Java EE 6, JBoss AS 7 and frameworks such as Arquillian, Java EE is a pleasure to work with.
