To be honest, I don't know if my glass is float or plate. I just went in and asked them to cut me a piece of 3/8 thick to my dimensions. I wonder if the difference would be significant in the distance over which we use it, and the way we use it? I do know that the glass I got works plenty good for my sharpening. I've put plenty of elbow grease into my glass when tuning a slick. No problem. I have the glass supported by an MDF frame/board, and this sets on my steel workbench. So long as your frame is on a reasonably flat surface, I think you'd be fine. Not you'd have this issue, but the glass does have a little flex to it before it would break, and I think the thicker you go, the stronger it will be. You could step up to 1/2 inch, but more than that is probably more than is necessary.

We have some plate glass piece here that we sell. I'd have to measure them to be sure of what the dimensions are before I comment on them.
If anyone is interested in a piece.

Glass is great, but the sandpaper needs to be glued well. I always stack another piece of glass on top of the paper I'm gluing and put some weight on it till dry. Also I use a straight edge to spread the glue as evenly as possible.
Even then, sand paper on glass is not like water stones, and I'll often see a bit of rounding at the edges of the surface I'm working on.

I use spray adhesive (3M Super 77). Afeter a few times, you need to scrape off the old glue with a razor blade. CB.