On the international CA flights, I don't think they will bat an eye if you have a regulation-size rollaboard or hand case, and another smaller item like a laptop bag, shopping bag, etc. They're not going to weigh the carry ons unless you look like you are a pack camel straining under the load. Particularly if you have a foreign face. That's if you are travelling in Y class. If in F/C, they wouldn't even bother weighing.
On checked bags, you have info above. Also, if you are *A Gold on any airline, for journeys to/from USA, you get an extra checked bag (i.e. 3 instead of 2) at the upper weight limit each.