Aztecs, Incas, and Mayans used them for their knives and other implement of war and everyday life. When they made knives for war they were thicker in dimension and had a more oval cross section. This provided a bit more strength. But, if they really wanted a thinner blade they would use flint or chert to make a stronger blade from. Not quite as sharp but more durable!
There are accounts of Aztec warrior slicing off horses heads with their sword like weapons (cant remember the name of them). Blades driven off a core where embedded into the edges of the wooden sword like device. Since they are around 2 microns thick on the edge they tend to more part molecules than slice through things. Something like 1000 times sharper than a surgeons scalpel.