I have checked tyres on EK before albeit over two years ago. My tyres were much bigger and I imagine mine would weigh over 32kgs if in a pair. If any package you try to check in weighs over 32kg it will not be accepted. You will need to repack into lighter seperate packs or send as cargo.
SAA has introduced a policy where you can't check car parts and I was actually refused to check in a wing mirror on SA and had to throw it in a bin at OR Tambo. Irritated me hugely as it cost almost £200. In fairness to SAA this was mentioned in small print on the ticket but I think the staff read too much into the rules. I can understand refusing some engine parts but mine was just a mirror in some plastic with a motor.