Thud hit the nail on the head. Weight plates vary in quality (and therefore accuracy). Some very cheap ones are sand cast from what is basically scrap metal. These aren't going to be very accurate, but they still provide an approximation and provide resistance. You can sometimes even find voids where the mold didn't fill properly.

Most of the brand name plates for home use are pretty accurate, not trade scale accurate, but within a percent or so.

Plates made for competition, sometimes called olympic plates, are made to exacting standards but are quite a bit more expensive.

Some gyms that specialize in lifting will have olympic plates but most find the mid-level plates close enough for training.

Be aware that many manufacturers like Weider, Golds and York make several lines of plates to meet different price points.

I'm in the camp that says not to obsess too much about the scale, it is only one indicator of progress. For instance, if over a few months you lose six pounds of excess fat and gain six pounds of muscle and other lean tissue, your scale says you didn't change when in reality there was a 12-pound shift in your body composition. I have the same problem with the BMI scale as a 6-foot, 200 lb athlete gets the same score as a 6-foot, 200 lb couch potato even though their level of fitness and body composition may be vastly different.