Well it depends on how much time you want to spend on it.
The wood dimensions rule out my original idea.
Assuming no restriction on height, cut 4 strips 8 inches long and 8 strips 315/16 long (yeah it's a bit accurate, you'd be better off just using 4 inch strips and ignoring the 1/16 overhang you'll get).
Now:
Lay an 8 inch strip
Put 2 of the shorter strips down to create a cross (should be dead centre).
Lay another 8 inch strip, across the 2 shorter strips so it intercepts the other 8 inch strip in the centre
Lay 2 short strips on the remaining sections of the first 8 inch strip.
Repeat this so you get four layers about an inch high.
You can test it without glue, balance something on the centre (if the weights are round and can sit on top of each other like you say there'll be no problem). Although it will be more rigid with some glue.
It's not the simplest idea, but it will give you good support. The downside is you only get 1 inch in height.
I have a feeling you're looking for something else when you say structure.