Are you on a stable surface? Could air currents be affecting it? Or could it be a thermal error as temps slowly change? This would be indicated by the readings going up by 3 counts every time you read it for awhile, you know, long time periods in the trends.
Sounds like you have a mechanical friction (maybe it could be called hysteresis) problem. There's little you can do about that, frankly. You may have hit the limits of that sensor. But it could also be the result of anything other than the load cell touching the weighing plate. Even lateral contact with a guide or whatnot will support some of the vertical force through friction.
This is why scales which measure 0.1 grams or below are considerably more expensive.
Burr-Brown (division of Texas Instruments) is the other big maker of ADC chips. They do plenty with external xtals.
I don't think your filtering strategy (that 0.3x + 0.7y) is valid. It does not filter well. That ADC reads something like 10 readings/sec. A 1 or 2 sec period isn't bad, but you want to do continuous updates. So you set this thing up to read the ADC as fast as it converts, put them in an endless buffer of the last 20 readings, and every 0.5 sec update the display with the last 20 readings for a 2 sec averaging period. The display update period and averaging period need not be the same.
What were you planning to do for a capacitive filter? You do remember the prob with sigma-delta ADCs and cap filters, right? What problem are you trying to solve? The only thing you have left is repeatability.