You only mentioned one of the two aspects of sigma-delta AD converters.
The one you spoke about is noise shaping, but you shouldn't forget about oversampling, which leads to the higher resolution.
Since this is the same for the other question, you should make yourself familiar with it, maybe you'll then get the clue

Thanks for responding.
As I read and familiarize myself more with all these concepts, I believe I have made more progress in my understanding.
In ADC oversampling with 1-bit quantizer followed by low pass filtering leads to increased SNR and thus may be interepretted as higher resolution than 1-bit even though a 1-bit quantizer was used makes sense.

However Sigma-Delta in DCO where the modulator output goes to DCO's discrete capacitors seemed a little different and therefore I was confused.

Here is my evolved intuitive feel for sigma delta modulator in regard to the DCO.
Keeping in mind the fact that average o/p of the modulator is same as the average of it's input and that the averaging happens in the DCO itself at the capacitors.
Say the input of the modulator is N-bit and it's output of M bits => 2^N input levels are possible. That also implies that at the modulator o/p there will be as many corresponding average values that are attained with the help of M discrete capacitors. Hence the M capacitors are pulse width modulated to increase the effective number of capacitors. That is just like the Fractional-N PLL with sigma-delta modulator, where say N/N+1 divider is pulse width modulated to provide finer resolution.

So returning to DCO, it is now much more apparent to me how the resolution increased with Sigma-delta modulator while saving space (+advantages of dithering) by using M capacitors which is much smaller than having 2^N discrete capacitors. 2^N discrete capacitors may not be practical anyway.