It all really depends if the check-in agent works for the airline or a third party handling agent. In my experience across most airlines and locations. Employees are far more likely to be rational, while 3rd party employees are not. OTOH, 3rd party employees CAN be overridden if you go about it the right way, while actual employees generally cannot be.

Regarding weights and tolerances. Lets say that each bin has a posted limit of 35kg (it is actually closer to 70kg on newer/bigger bins). If we are talking about standard trolley bags, and talk about Two per bin, that means 17.5 kg PER BAG, if we are talking about three bags, then we are talking about roughly 12kg per bag (and something unlikely as my experience of LH overheads is that you cannot fit 3 in there), so yes, in fact exceeding the limit by 50% is not a problem no matter how you frame it). And BTW, the actual structural limits are in fact TWICE the recommended limits.

Lastly, European carriers have always had a thing about weight. Forget 9/11, monetization and everything else. US carriers traditionally went by the piece concept, while Euro carriers went by the weight concept. For US carriers standard was always 2 pieces at 70 lbs per piece (32kg) - Three in Biz. While for Euro carriers it was always 20 kg (later 23kg) and 30 kg respectively.