You can certainly have a resolution within your limit of 3 gms when your FSD is 2.2 Kg, so that isn't a problem. Your problem is more with stability in the rest of your system than the ADC technology to begin with.

Using all the ADC's range 0-1024 for full scale means that the basic zero stability of your electronics must not drift by more than 1/2 lsb of your ADC. You will have no software tare facility with this approach.

Steve