Steel does not just simply hold the weight, up to the limit, and then break.
It stretches elastically at first, up to what is called the yield point.
When loads less than this are added and removed, the steel will stretch, but then return to its original length when the load is removed.
If a load greater than this is applied, it will stretch but remain stretched after the load is removed.
See this Wikipedia link: <Wikipediai/Ultimate_tensile_strength#Ductile_materials>
The actual breaking point is actually slightly higher than the yield point.
So an engineer would be looking to keep the loads below the yield point of the material (and they would also include a sensible safety factor).
However, the exponential nature of the weight to height relationship will remain, regardless of the actual limit point chosen.