doesn't it add significant weight to the price ?

They simply adjust the tare weight in the scale and that's it. They do it anyway with their own 1-use plastic boxes or sheets.

I've never seen a meat counter employee re-zero the scale after putting a container or wrap on it. I do occasionally see them reading -0.1oz or something initially, presumably to avoid the need for the employees to zero it out each time they weigh something.

My feeling is that they have a few presets available for the containers they use, but it totally can be changed to a custom one.