I checked the websites of Northwest, Delta, Southwest, American and United. They all said the same thing:
Maximum weight of each checked piece: 70 lbs/32 kgs. Maximum size is 62 inches/158 cm, using linear measurement which is length plus height plus width.
Since they all say the same thing (and in the same language), I think it is either an FAA rule or an agreement between the airlines that they will all stick to this. Southwest and Delta had their excess weight charges posted; it was sort of a formula based on how many bags you had and how many were overweight. From Delta's website:
"We charge an excess baggage fee if you have more than two pieces of baggage, or if one or more of your bags exceeds the weight or size restrictions. For example, if you have an extra piece of baggage that exceeds the weight limitation and the size
limitation, then you will incur the excess charge 3 times - once for the extra piece, once for exceeding the size limitation and once for exceeding the weight limitation."
Their excess baggage fee was $40 for an extra bag, $80 for excess weight and $80 for excess size. So their example above (a 3rd piece of baggage that was overweight and size) would be $200.
I think this was one of those things that was always in place (I remember my parents weighing their bags before they left on trips when I was a teenager), but not really talked about much. Extra weight means the plane needs extra fuel, which someone has to pay for. I do know that we have had foreign exchange students who have paid an excess weight fee when they went back home because their bags were too heavy. After the first time that happened, we have always weighed our bags before we leave home.