Welcome to the forum, Al, and congratulations on your "new" trailer!
An empty fiberglass shell is quite flexible. That does not indicate a problem (unless you leave it that way). Reinstalling the cabinetry will make it solid again (you may have to gently raise the center of the roof to restore the original shape to make everything fit right).
With a single-wall fiberglass trailer, pretty much every piece of the original interior cabinetry serves a dual function as structural support for the shell. That 1/8" is about right all over. Scamp
does add additional layers of fiberglass (but no wood) on part of the raised roof to prep for an AC installation. It's standard now, but most older models don't have it.
If you do not plan to reinstall the original cabinetry, you need to reinforce the walls somehow. If you just beef up the roof, adding more weight
on top, the walls will tend to bulge out even more. Among other things, the door may not fit properly.
One way to reinforce the walls and roof without a lot of weight
or bulk is to glass in ribs. You might want to read member Ian G's thread It Started as a Kitchen Reno
. If nothing else, it will get your creative juices flowing!