In my many years of flying TG, the only absolute limit they have implied is the 32KG per piece allowance. They'd not budge on that - health and safety rules.

Though I have been gold with TG most of my flying life, so I never had this problem, watching check-in at different airports, it's doesn't seem to be been an issue upto 5 or even 10 KG extra, but always a NO for anything above 32KG.

Cheers.