I just noticed that the baggage weight allowance says 50 lbs or 23 kgs.

50 pounds does NOT equal 23 kilograms!

23 kilograms is roughly 50.6 pounds at 2.2 kg per pound.

How does AA deal with this little detail for people who might be just over 50lbs, but under 23 kgs?

Yes - the scales at the check-in counter probably aren't that accurate to being with, but the discrepency is still interesting.......