I believe that the trucking portion of handling the container has weight limits; the machinery that handles the loading and unloading have their weight limits; the ship and the way it is loaded from bow to stern has weight limits, and a container itself has weight limits. Somewhat analogous to freeway overpass heights, the tendency over time is that the various limits harmonize with each other and you get typical shipping practices.

A shipping container full of raw cotton is indeed quite different than one full of "iron ore" but actually, consumer electronics and various car parts, their load limits, are more commonly restricted in the way they are loaded and handled.