Applying aspects to POJOs could be actually a reason to call EJBs "heavyweight". But then, all other frameworks will have to be renamed as well :-). One real issue with J2EE were overblown (often commercial) appservers. The deployment was slow and errorprone. However this issue is already solved (the download of Netbeans 6.1 with Profiler, Visual Designer, Tomcat 6 and Glassfish v2 takes 139 MB) and is getting even better. A deployment of a small EJB 3 takes about 2 seconds on my machine (without virus scanner :-)), bigger applications can be deployed in less than 1 minute. The only thing, which takes long ist the preparation of NamedQueries in JPA - but this is an EJB 3 independent issue. Glassfish v3 is highly modular and embeddable. JBoss - was always modular - and is embeddable as well.
So, what's the deal with "lightweightness"? If you ask me, EJB 3 are "ultralightweight", and POJOs actually silently disappeared. The "POJOs" are often nothing else, than JavaBeans maintained by another container, using similar techniques. Pure POJOs, without decoration, configuration and aspects are gone (or are only usable in applications without concurrent write-access to database). Even ultra-lean (and really great) Guice, will have to decorate POJOs with transactions, concurrency, inject resources etc. Perhaps we should rename EJB 3 to another term - the same story as with applets - the problem with the history :-)