Hi Dhinesh,
If you have a 600 gram load cell and need to measure at 10 mg increments you need 60000 noise-free counts. There isn't a lot of margin but this may still be achievable.
If we have 8mV scale defelction at full-scale, then we need to measure 8mV/60000. This becomes approximately 133nV increments. The LSB size for the ADS1230 is 5V/128/(2^20-1) which is approximately 37.3nV. If we divide 133nV/37.3nV we get approximatey 3.5 codes per step. This is about 1.8 bits. This gives you a margin of 0.3 bit assuming you use the calculation example from the datasheet (17.5 bits + 1 bit from averaging.)
The best the ADS1230 can do at 10sps and gain of 128 has 198nV peak to peak noise. So you will not see the desired 133nV resolution. Adding external noise will make this even worse. You may have to average a lot to reduce the noise. Usually going beyond 100 averages you will start to have issues with drift. I would try 50 and see if that works. Even with many averages you may still see the count change as there is no partial bit in the conversion result.
Another thing to consider with respect to performance is your board layout. What kind of prototypoing system are you using? You cannot expect to get high levels of performance with breadboards. You need a well designed PCB with proper grounding and layout.
Best regards,
Bob B