Florian Cajori's A History of Mathematical Notations goes into the history and notes examples of old written manuscripts showing the intermediate form in use, with one example where both were used interchangeably in a letter. He examined the question in depth, showed that the earliest uses in the US had a single stroke, with the double stroke only coming later, and dealt with the other theories showing as conclusively as possible that it's a peso sign composed of a superimposed P/S. It's an old book, and not on a web site, but you could probably find a copy at a library.