A similar comparison of weight between plug-in hybrid and gas motor models in the FCA line is the Chrysler Pacifica, the latter of which is 657 pounds heavier. If anything near this additional weight is added to the JL then it is going to be pretty heavy.
I have no personal experience on either, but autoblog.com shows the 4-door JL being only 72 pounds lighter than the 4-door JK. Though not expressed in my post, my qualification as "heavy" was in relation to TJ and LJ Rubicons which are listed as 706 and 472 pounds lighter than the 4-door JL. A Chrysler Pacifica plug-in battery weighs 500 pounds so I imagine the JL battery may be in that ballpark.
So, I am curious how much the plug-in hybrid JL ends up weighing.