Well, in that case you may want to concentrate in zero drift and make sure the linearity does not change with temp.
For a counting scale the precision is irrelevant, only zero and linearity matter. A very cheap means of zero compensation is a pushbutton that must be pressed with an empty scale before measuring can commence. If that is not acceptable, make power up do zeroing - remember a warning message if the adjustment is too great (something on the scale) - and find the minummum weight you will weigh and rezero whenever you are below that weight. If your weighing ratio is anything more than 8 bits, you must be EXTREMELY careful in laying uou the analog section and you will most likely need a chopper stabilized op-amp as your front end.

Not trying to scare you, just making you aware.

Erik