As you may or may not know, Kentucky, Virginia, Pennsylvania and Massachusetts style themselves as “Commonwealth” not State.
According to Ben’s Guide to the US Govenment for Kids, these four subdivisions of the United States government chose a term meaning an organized political community as part of their constitutions. The choice of word perhaps harks back to the “Commonwealth” of England from 1649 to 1660, when the mother country was a republic, thus it was a choice to be completely separate from the old royalist “state.”
Another reason for choosing this term could be its literal meaning of the common weal, or well-being, of the inhabitants, and the orginators intended their communities to be governed for the common good as opposed to an authoritarian state governed for the benefit of an aristocracy. Virginia, for example, was a “Commonwealth” before the Revolution.
Or perhaps they just like the sound of it.