Rails come in different sizes. The most typical is 130 lb/yd. But, there are several sizes that are used. I have no idea how much weight it would take to bend them, but I do know that temperature has a lot to do with it. Sometimes they will warp on their own with the right extreme temperature changes. Don't ask me how, but they do.
Edit: Called a friend who works for Norfolk Southern, he said that if they are on cross ties spaced as per specification (about 40 ties every 65ft) that they can hold over 1 million pounds. He said they are much easier to bend side to side, and that is why they will warp on occasion.