Rule is two bags to total 16kg/35lbs in Upper Class, one bag 6kg/13lbs in Prem Econ/Econ.
Codeshare irrelevant - operating carrier always sets the rules for such things.
I have yet to comprehend why (a) my heavy overhead bags are less dangerous to myself and others if I paid for a higher fare clase, or (b) the Europeans are so bloody more uptight with carry-on restrictions than the Americans.
Agreed with the previous poster - I swear my case is within 1 kg of the limit when it's completely empty!