Capt Fathom has hit the nail on the head:
Unfortunately, if the loadsheet says your 1 kg overweight, you have to get rid of that 1 kg!
In days gone by, the problem might have gone away with some creative accounting but in this age of litigation and disengaged workforces it's a no brainer. While it is usual practice to offload deadload before pax (and assuming nil cargo) pax are heavier than bags so you will upset fewer customers by offloading pax before bags. If you offload the required weight in randomly chosen "last on" bags and have the courtesy to advise the affected pax, you run the risk of an even bigger bun flight than if you "appoint 2 volunteers". Was there also a trim issue which determined the chosen solution?