Weird reading from NAU7802 ADC
Aha, I finally found the answer in this code!

The datasheet mentions a couple of "choppers" - ADC chopper and PGA chopper, but doesn't really say what they are and at least in the case of the ADC chopper there is only one value that isn't reserved (off). It turns out the non-reserved value isn't the default! If you turn off the ADC chopper it gets rid of the weird triangle wave. A small amplitude sine wave remains, but if you turn off the PGA chopper that goes too. Here is the relevant code (writeReg is the obvious implementation).

writeReg(OTP_B1, 0x30);
writeReg(PGA, PGA_OUTPUT_BUFFER_ENABLE | PGA_PGACHPDIS);


Stupid datasheet.