In its original sense in English, sad had the meaning “fully satisfied, sated.”
From this sense it underwent alteration, as so many English words do, and came to have the meaning of “solid, heavy, dense.”
It is in this sense that it is used in the sadiron, which is a heavy, solid flatiron used for pressing and smoothing clothes.
Regardless of how sorrowful the housewife may be that she is compelled to use this weighty tool, her sadness has no part in its name.
