Having spent some time hanging out in paper mills (babysitting control systems), I suspect the 'ply' relates to adding multiple layers of the wet pulp down in sequence to build thickness. But the created plies will likely have pretty much merged and disappeared by the time the finished product goes through the many rollers. It is also likely that in modern processes they may not lay down four distinct plies to get '4-ply' thickness.
There are some mind-boggling bits of arcane terms and dimensions in paper making, partly thanks to it being rather ancient technology. Even the pounds per ream is screwy in that paper for different applications may use a different sheet size to calculate the weight. Most stuff now seems to show grams per square meter which is a lot more consistent in that regard.