American only imposes a 20lb weight limit for carry-on pets if you'd want to bring them on board in the premium cabins on the three-class Airbus A321T which flies select transcontinental routes only:
https://www.aa.com/i18n/travel-info/...ontinental.jsp All other cabins and routes only have carrier size limits but no weight limit, the same as with Alaska.
Depending on the airport you transfer from Alaska to American, you will have to exit security and go to an AA check-in desk in order to process your cats with AA and pay the fee. Normally there is no weight check, just a visual check..