4gram noise independent on the weight
Of course, you do noise has nothing to do with how big your input is.

I believe that you have been overly optimistic re the dynamic range of your weighing system, if you want less noise than, say, 1 bit in 12, laying out the PCB is not a skill, it is an art.

I made an entry in the FAQ <--- about noise, not specifically analog, but to get any better than 1 bit in 12 you need follow each and every rule PLUS make a 'perfect' PCB layout.

Erik