To all of my knowlegable, and esteemed colleauges.. I would like to throw out another possibility as to what these are... Right now, the group is pretty much split, 50/50 on cannonballs and milling balls.. I have to say, that I know what these are, and how they came to be...
First, I will confirm that they are old... I will also confirm that they are Spanish... but they are not cannonballs nor are they mill balls... While doing some research

, I found that this is a horde of... wait for it... BOCCE BALLS!!! Yes.. these are the missing bocce balls from the 1st Annual International Coed, Clothing Optional, Bocce/Yard Dart Championships of 1491..
Not unlike hockey, the rules state that the home team (the Spanish) are required to keep a certain amount of bocce balls and yard darts on hand. Unfortunately, the equipment manager, Francisco Allehandro Cesar de la Jesus misplaced the key

to the bocce/yard dart equipment shed right before the championship match.. The other teams, who felt cheated out of their chance at glory, fame, girls

, and all the free Spam

that they could eat, left in a huff.. This caused an international incident

, and was thus ordered by Queen Isabella of Spain

to be stricken from the history books and to never be spoken of again, lest the guilty party be brought into the city square, and smacked about the head and chest area

...
I hope this bit of research has helped.. btw.. keep looking.. those arrowheads that we find in the plowed fields arent arrowheads at all.. You have stumbled into one of the team's lawn dart practice areas...
GL & HH