The number of axles on a car determines the maximum weight. Each railroad has specific maximum allowed weights depending on their infrastructure. When I worked on BNSF, we were allowed to have cars up to 143 tons, which is 286, 000 pounds, but we were allowed to have a certain number of overweight cars, loaded to 144 tons, as long as they were not next to each other in the train.
On Alaska Railroad, 263,000 pounds is the maximum, but again, we can have some overweight cars in the train, up to 268,000 pounds, as long as they are not coupled to each other, and as long as there are not more than five in the train.
All of the above weight restrictions are for typical, four axle freight cars though. When it comes to specialty cars with more axles, things are different. Usually specialty cars fall under the "Excessive Dimensions" category and must get special clearance over the intended route prior to moving, especially if they are overweight. We had a 20 axle depressed center Schnabel flat car in Alaska last fall to move some generators. The maximum weight stenciled on that car was in excess of 900,000 pounds, although the loads it carried here were just over 500,000 pounds. It was well below the weight limit for the car, but prior to moving that kind of a load, someone had to verify that our bridges could handle that kind of weight, even spread out over 20 axles. Every time the train ran with that car loaded, there were speed restrictions placed on it, more speed restrictions on a couple of the larger bridges it crossed, and the crew had to have clearance paperwork because the weight was considered an excessive dimension.
So it can be done, but extremely heavy cars are pretty uncommon.