The UK and Ireland use stone weight as human measurement because it has to do with stones that were used years ago for weighing things and people.
Basically the scale that the person or thing was on used a stone or stones hung onto the other side and when the person or thing was balanced out by the stone they would be considered that many stones in weight.
For example if you stood on the scale and it took 14 stones to balance your body weight out then you would be 14 stones in weight.
Ireland and UK still use the stone weight saying because I guess it just stuck with them.
Although it can be confusing to people in the USA.
But it does literally have to do with the stones that were used many years ago for the scales.