Dick, I'm pretty sure your ceiling is cored, not sure which year they started coring. Just press up on the ceiling, if it's stiff, it's cored. The 5/16" ceiling like mine is easy to flex -- but maybe an advantage of less weight above the waterline.
I will be adding arched aluminum or SS stiffeners to my ceiling to support the extra weight of the rods/reels. Although not that much weight, I have noticed some sagging in the summertime when it gets hot inside the cover, so I temporarily support the ceiling with an extension pole when stored.