If my memory serves me correct, is the floorings flip side the flooring that is exposed to the underneath open area?
If it is, then I would use a treated ply wood like a marine ply or use Treated ply.
Whether to replace the weak spots or just the entire room? Well, what has caused the weak spots to become weak? Is there an appliance in that area? If this is only due to wear and tear, then I would say do the entire room, but if its due to an appliance leaking and is just ISOLATED, then the weak spot.