It makes a difference where you are comming from, and where you are going to.

North american flights usually read line the AA website as I think there is airline discression,

Transatlantic reads line the LH site, where there is some treaty in effect, and 2 x 32kg is the rule, although an extra may be allowed.

Inter European is again airline discressionary.

It is cost effective to carry extra bags rather than overweight or oversized bags.