While the size limit for carry-on baggage is roughly the same for all the US carriers, usually in the vicinity of 56cm x 35cm x 23 cm, there is no weight limit in most cases.
Neither American Airlines nor United Airlines even mention weight limits for carry-ons on their websites while Delta's own website states: "No maximum weight applies to carry-on baggage", except in the case of flights to some Asian destinations.
British Airways says the maximum weight for carry-ons aboard American Airlines, its oneworld alliance partner, is a healthy 23 kilograms, which is about the same weight limit that applies to checked luggage, effectively doubling your baggage allowance.
One exception is Hawaiian Airlines, which stipulates a maximum carry-on weight of 11.3kg.
Even this is in stark contrast to airline regulations in the rest of the world, where the weight limit for carry-on bags for economy class passengers is generally 7kg, with a few raising the bar to 10kg.
The US low-cost carriers such as Spirit Airlines and JetBlue, known for charging fees at every available opportunity, do not limit the weight of carry-on baggage, although Spirit applies a fee for even a standard carry on.
JetBlue adds the caution that while no weight limit applies, no assistance will be forthcoming from cabin crew if it doesn't fit under the seat in front of you. If you pack your carry-on case with geological specimens, it's up to you to heave it into the overhead bin.