I am hardly ever overweight on luggage. However, on the only recent occasion that I was (only v slightly over, less than 1kg) I politely queried when the scales had last been calibrated.
I was immediately let off from paying for the extra (this was a LCC). Now that could have been because it was so marginal; it could have been just a kind member of staff; or it could have been that the staff member was herself doubtful about the accuracy of the scales. Who knows? But I'll be trying the same thing again in future.