The Zapotecs were weaving in the valleys of Oaxaca as long ago as 500 B.C. The Aztecs conquered them and made their textiles into a tribute item for the Aztec empire. After the Spanish Conquest the Zapotec weavers were put to work by the Dominicans which were the dominant sect of the Catholic church in this part, indeed in most parts of Mexico.Many weavers still use the natural dyes to make the rugs. See my post on cochinilla here.
Many of the textiles for the table or shawls (rebozos) and other types of weaving are still made on back strap looms that those pictured here, you can still see the Triquis in the market using these.