Why EU/US airline checked baggage allowance limited at 32kg? For most full services on EU/US airlines, the permitted weight of each of the checked baggage allowance is 32kg. It is similar for the routes operated by non-EU/US airlines, even though their overall checked baggage allowance is more than that. What are the reasons behind that?
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.