For a cake that size, I would use at least 1/2" thickness plywood or something equally sturdy, regardless of the weight of the board. It will not be anywhere near as heavy as the cake.
It’s been some 40 years since I made this one — sorry I can’t remember what type of board we used:( but as you can see it was at least 1/2” thick (& 40” long) 
i use foamcore board, quarter inch and half inch -- might not be big enough so what i'd do is i'd actually make two boards -- i would buy three boards and cut the extra one to piece together to make up the size of the boards i needed -- piece each single one together with real wide tape into whatever size i needed -- then i would layer the boards together with the pieced in parts opposite each other -- so none of the taped seams took any stress without having the other solid layer next to it --
in fact what it morphed into was i would make the second board the exact size of the cake, again with the taped seams opposite the other board -- with the bottom board of course needing to be bigger to have the ledge around the cake -- then i could have the bottom board all decorated and ready weeks in advance -- all it needed was a cake -- and i would glue gun them together or use icing -- lots of times i delivered the cake separate from the bottom board and just assembled on site -- no worries -- if i delivered with both boards assembled, i used hot glue -- if i assembled the boards together i used a blob of icing ~
SO much lighter and easier to deal with
if you scroll down through this -- you'll see this demonstrated in pictures about a quarter way down
Demo: Making a wedding cake at home - Pastry & Baking - eGullet Forums
I meant, "if I assembled the boards together *on site on the cake table at the venue, I used a blob of icing"
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