I'm not sure why you assert that Dropwizard is getting heavier. The difference between this release (0.8) and the previous one, is just about bumping up a bunch of libraries' versions and the big move to Jersey 2.
DW is essentially a collection of libraries with sane defaults and some plumbing, so I don't see how you can compare it to JEE. JEE may be lighter these days, but it still requires a container to run - unless you use the latest incarnation of the IBM JEE server, Liberty.
Dropwizard also requires a container to run. Only difference is, they are bundling a particular container (Jetty), as opposed to the model of deploying into a container that you set up.
I think you're using the word "container" when perhaps "app server container" is more meaningful. An app server container (like Tomcat, WebLogic, WebSphere, etc.) typically provides services (database connectivity, persistence, management, etc.) to the applications deployed into the app server container, where the benefit is especially useful when multiple applications are deployed in the same container (though in my experience, this is often where problems occur and people end up deploying separate app servers per application).
Dropwizard is meant to run without an app server (aka containerless), and uses the Jetty embedded web server (which is not an app server container) to provide the HTTP communication.
DW is essentially a collection of libraries with sane defaults and some plumbing, so I don't see how you can compare it to JEE. JEE may be lighter these days, but it still requires a container to run - unless you use the latest incarnation of the IBM JEE server, Liberty.