Are the bases vacuform, like the old Airfix diorama bases? If so, there are a couple of options.
The heaviest is to fill them with plaster or putty. A 2-part epoxy putty would work. The lightest is to cut pieces of styrene sheet stock to make braces, and glue them to the inside of the base, creating a framework like the joists in a floor, to add some rigidity. You wouldn't need for the top of such a brace to meet the contour of the base all the way along its length. It would be sufficient to glue a straight piece across, and then glue smaller pieces vertical to the brace and touching the base, at intervals.
Of course, if the bases are fashioned some other way, then my suggestion is probably not relevant. But I hope it helps.
Prost!
Brad