Glue for a plywood sandwich?

[Bill Stock]

I want a sheet of plywood 8x12. So I thought I would glue two stacks of 1/4" plywood together, offsetting the seams as much as possible. This will be exposed to the elements but s/b protected from direct rain/sun. Will some kind of contact glue do the job or is there a better (cheap) option? Any better ideas for a single large light sheet? I thought T&G would give me a better join, but I don't know how thin I can get this or how it would hold up to weather.