The ADC is powered from a DC/DC converter followed by a filter.
Avdd and Dvdd are powered from a different DC/DC converter.
With an update rate of 200Hz, 10mV bipolar input range, chop mode, you can
expect 80nVrms of noise or about 15-bits of noise free resolution. If you are
only seeing about 9 or 10-bits of noise free resolution, I would guess that the
DC/DC converter is probably feeding through to the converter and adding noise
to the conversion result.
As a first test, ground the analog input pins (remove any input conditioning
circuitry) and disable the DC/DC converter. Use a clean bench top power supply,
or a battery plus linear regulator to power the AD7730. You need to ensure that
the DC/DC is removed from the system as noise could be coupling into the ADC as
ripple on the power supply or as radiated emissions. By doing this, it should
be possible to achieve the datasheet spec for resolution.