The values are not always the same when applying the same weight.
Can you be more specific?
The analogRead() fluctuates, to stabilize one might connect AREF to 5.00 Volt.
Or take multiple readings and average them;
x = (analogRead() + analogRead()) /2;
Or use a "low pass" filter : prev value is used for 90% and the new value is used for 10% (percentages can differ, watch out for int overflow)
x = (analogRead() + 9*x)/10;
Will a scale like this keep a steady measurement without major changes over time?
Good question, do you have a link to the datasheet? maybe it makes some statements about continuous use.