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The standard kilo was/is stored in a vault inside several bell jars and only removed once every ~30 years to compare with the world's national reference/transfer standards.

As far as I know, the mechanism by which Le Grand K is drifting with respect to all of the national references is not known.

To leave it on a balance (which must be operated/checked/maintained) would expose the K to much more risk.

At this precision you weigh things twice. Once with the reference on the left arm of the balance and the test object on the right and another time with objects swapped.

The balance still would need to be balanced.

right...

and then left...

I think they needed to take the replicas from other countries like the US to the master one in Paris for comparison every year.

Edit: see this Veritasium episode https://youtu.be/SmSJXC6_qQ8

Also relevant: https://www.youtube.com/watch?v=ZMByI4s-D-Y