How do I go about making 1" and 2" thick "boards" for concrete furniture?
I did go ahead and pour a board, and have the results.
I was told sand filler instead of gravel for &lt;= 2".
I went with just the default sand filler blend and thin steel rebar mesh (wire basically) at my local hardware store.

A 1.5" board that was about 4.5" wide and supported at 2' intervals supported 110 pounds. I had decided prior that 80 lbs would be acceptable.
I think this means that I guesstimated perfectly. A 2" board should be acceptable for high-wear areas (I am hoping it would take about 200 lbs), 1.5" for medium, and 1" for light.

So it is heavier and does support less than a wooden board. But it has some benefits (in my case it is not chewable), and only costs a couple bucks for materials.

Even better was its fail state, 110 pounds produced a hardly perceivable hairline crack on one side only, held together by the rebar mesh.