Why EU/US airline checked baggage allowance limited at 32kg?
To add to Antzi's answer it is most likely about worker safety. Your question is where do the 50lbs/23kg and 70lbs/32kg numbers come from. The current answer for US based airports would be the recommendations of the Occupational Safety and Health Administration (OSHA). Here is a link to their current lifting standards. There is a neat worksheet down at the bottom for calculating the weight a worker should lift based on the types of movements they have to perform, distances traveled, angles bent. It is a system based on multipliers whose base limit on a normal lift is 51lbs/23.4kg. Then 70lbs/32kg would amount to the multipliers all working out to 1.4 which is again a nice round number. 

I would also speculate that at some points these numbers made it into union contracts for ground workers but I have no actual information on that.

What I couldn't find were the OSHA regulations that were in force when IATA first enshrined 23 and 32kg into their rules. It is perhaps a bit disappointing that the current OSHA regulations to not have a "max lift" number but their interest is in reducing injury and a single very heavy lift is apparently less damaging than repetitive above average lifts.