Here's the breakdown:
* Latin "pesare" > Italian "peso" (meaning "weight") > Spanish "peso" (meaning "weight" or "currency").
The Spanish adopted the word "peso" to refer to a specific weight of silver used in their currency. This usage then spread to other Spanish colonies, including the Americas, Philippines, and other parts of the world.
So, while the word itself is Latin, the Spanish language and culture played a crucial role in its evolution and adoption as a currency term.