American Airlines: standard limit is 50 lb per bag — overweight or oversized bags cost extra on top of the regular baggage fee.
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51-70 lb: $100-200 extra, per bag.
71-100 lb: $200-400 extra — most routes cap checked bags at 100 lb entirely.
Over 62 linear inches: around $200 extra, per bag.
Weighing your bag at home with a luggage scale before you leave is the single easiest way to avoid this fee entirely.