One place I worked would bolt a sheet of steel in the bed of their trucks and then lay a rubber bed liner type mat over it. About 3/16" steel I think. It added weight, added strength to the floor of the bed and had no effect on use of the bed except of course for the added weight. It was bolted down, so not going anywhere so long as you use an appropriate size and grade of bolt. It really helped tame those trucks on washboard roads. When they sold the trucks, they pulled the plates and bed mat, it left the truck with a fairly straight bed with a few bolt holes in the floor.

3/16" sheet steel weighs about 7.6 lbs/ sq foot, a 4x7 foot piece would weigh 212lbs. 1/8" steel weighs 5.1 lbs / sqft, so a 4x7 sheet would weigh 142lbs.