The stone has meant various weights at different times, including 24 pounds and 25 pounds before settling at 14 pounds. I don't believe it had anything to do with a monarch, but rather the fact that actual stones were used in balancing weighing-machines in market-places. One was referred to as the Stone of London.
I guess it was seen as the master-weight in much the same way as, today, standard weights and measures are kept under lock and key in various places. If I remember rightly, the master-kilo is held in a Parisian vault, for example.