I really would like to meet the first airline pilot who has never done a overweight take-off in his life, be it unknowingly...
Remember that only average weights are used for most items on board, so figures like TOW=125.435kg on your final loadsheet are totally pointless; your real TOW could well be as low as 124.000kg or up to 127.000kg! Now, for flight preparation and planning this is not much of a problem, but if your certified MTOW is 126.000kg, then it might very well be that although according to your loadsheet you are ok to go, you are actually 1 ton overweight!
You see what I mean?
Now, 1.OOOkg may look a lot to most of you, but on a plane weighing 150ton, this is less then 1%!
It's exactly the same as having loaded 3kg too much on a Cessna 150...
Oh, before someone asks, no I have never ever seen a loadsheet where they take a margin on the MTOW to compensate for the inaccuracy of their approximations. If your certified MTOW is for instance 56.345kg, then they may/will load you up to that figure, notwithstanding all inaccurate average values used...