Inferring DC performance from a Sigma Delta ADC datasheet noise floor figures
You have certainly started looking in the right places, and are making sensible observations, but the world of interpretting ADC specs and real world performance needs some experience.

Looking at the data sheet FFT presented, the -80dBc spur is clearly a harmonic of the 50Hz fundamental being measured. It's at the right frequency and well out of the noise floor. This will not be present when measuring DC.

More relevant is the noise floor, shown at a level around -100dBc, but this requires careful handling. The -100 is the amount of power in each FFT bin, however as we're not told the length of the FFT or (equivalently) its noise bandwidth, that's meaningless. What we do have are the summary figures in the top right of the graph, which gives SNR (signal to noise ratio) as about -74dBc. This means the total integrated noise across the DC to 4kHz bandwidth, excluding that 100Hz spur, is 74dB below the full scale fundamental power. That's double the rms voltage of a -80dBc signal.

While it's relatively easy to estimate the voltage of a signal spur, it's repetitive, a clear peak to peak, and independent of bandwidth, the same is not true of noise.

Your observation of about 80mV noise is difficult to use, on two counts. The first, the peak to peak of noise is ill-defined, and rms noise is difficult to estimate by eye. The second, what is the bandwidth of the noise? This even more difficult to estimate. Whereas a spur is independent of bandwidth, noise power has a 'per bandwidth' density. 

If we assume that either you're looking at a graph of the full 8ks/s readings, or some points selected from those, then the effective bandwidth is the full 4kHz, and you would expect to see the full -74dB noise power. If any averaging is happening, explicitly or implcitly, then less.

In the context of your scaling, a -74dBc figure for noise would be rms voltage of around 100mV.

The usual practice for DC observations is to do some averaging of the points read out. This reduces the noise bandwidth, and so reduces the noise power. It's often said that averaging 2 readings together gives a 3dB improvement in SNR. This is true while the noise floor is flat. 

Take a close look at the noise floor in the FFT in the range below 200Hz. The noise floor starts to lift towards DC. This is common amongst all types of semiconductors. What this means is that once your filtering has excluded all the flat noise above 200Hz, you will see less and less improvement as you reduce the bandwidth further. The effect that you see, you may interpret as 1/f noise, or at longer time scales, drift, rather than added noise.

Users and manufacturers of low noise opamps aimed at precision DC applications have a hard time interpretting noise and drift for their products, often showing time domain graphs filtered to a 0.1Hz to 10Hz bandwidth. Find and read a few data sheets for this type of product if you're interested.