Hi levsmith,
As a retired engineer, listen to angib on his discussion of sandwich construction. I was going to reply with essentially the same info but luckily I saw his post first. Saved me a lot typing
Years ago I made a sample piece of 3/4" XPS Styrofoam with a single layer of epoxy glass on both faces and I used it as an example to show others how stiff and strong it was. Unfortunately I lost it but more recently I needed a simple lap table for my computer and all I had available was a piece of Styrofoam and a roll of builders kraft paper. So I laminated some of the paper to the foam faces with carpenters glue and now have a very lightweight lap desk. As others have pointed out, it is the skin that provides most of the sandwich's rigidity and strength. Think drywall, the strength is in the paper faces, the gypsum core wouldn't be able to support itself without them.
If you want to mathematically convince yourself, the formula for calculating the moment of inertia of a rectangular solid beam is I = b h^3/12 where b = width and h = height. This calculation is used for computing among other things, the deflection of beams given various loadings.
For a sandwich construction with faces of the same thickness, just calculate the moment of inertia for each face with the height measured from the center of the sandwich. To save you from the math, it will nearly be the same as a SOLID pice but significantly lighter. However, to indemnify myself from a lawsuit and forum arguments, there are caveats. Specifically the foam must be stiff enough from crushing or excessive elastic compression and be strong enough in shear stress. In normal Foamie construction, those considerations don't come into play unless someone wishes to tap dance with stiletto high heels! For the trivia minded, the floors in airliners are sandwich construction but with a thicker top face so someone in stiletto high heels won't punch holes in the floor. I guess someone must have done that some time ago as I'm sure the male engineers at Boeing wouldn't have though of that. If they could, I'm sure the airlines would Ban stiletto high heels so they could save the extra weight of the thicker top face.
For your lightweight motorcycle trailer, I think a floor with some high quality 1/4" plywood faces over 1-1/2" XPS Styrofoam would be all you need. By high quality plywood, "Baltic Birch" would be my choice. Baltic birch ply is available down to 1/8th inch and even thinner. I've seen small pieces in hobby stores 1/16" thick. Epoxy would be the best glue but Titebond 3 wood glue should be enough and lot cheaper.
Hope I haven't bored everyone with my engineering lesson. Good riding with you favorite buddy. Be safe.
-- Teri