Lots of industrial electronic hardware mounts to DIN rail. I would think there must be a weight limit to such mounting. But I haven't been able to identify one. Is there a defined weight limit, either by written standard or accepted practice?
You can't find any maximum weight specification for DIN rails because there isn't a need for it. The maximum weight is a property of the mounting clips, not the rail. The mounting clips are designed such that they will always fail long before a properly used DIN rail will. If a DIN rail specifies a standard clip, then it means it can support at least the maximum number of those clips that can fit, each with a full load. So basically DIN rails are 'idiot-proof'. If you can fit it on and the clips will hold it, then you're good.
Every clip on the other hand DOES specify a maximum weight capacity, so you only need to worry that a device isn't too heavy for it's mounting clips. The rail can't fail because the weakest link in the chain are the mounting clips. And even if one used 'creative' means of putting extra weight on a rail, I would expect that the rail itself would rip off the backplane before itself were to fail anyway. For steel rails, their weight capacity is simply 'enough'.
Now, this is assuming the DIN rail is not being used improperly. DIN rails are sold in fixed lengths for a reason, because those lengths when properly mounted to a backplane can support the maximum linear kg per length along it that could potentially happen for the heaviest duty clip size it specifies. If you are doing something like welding two rails together or clamping them to span an unsupported length, then bad things will certainly happen. They're idiot-resistant I should say, not proof.
For this reason, you will find aluminum DIN rails that specify a smaller range or usually just a single clip style that can be used with it, even if there are other mounting clips that physically will snap on. This is due to weight: aluminum rails are not nearly as strong, so they will specify only the smaller mounting clips to prevent too much weight from ever being put on the rail.
One final note: This is not taking into account vibration. If something vibrates and the center of mass is an appreciable distance from the backplane, expect to derate the clip's weight capacity. Sometimes a lot. This is a specification that you also can find for clips, but less common. Don't use a mounting clip that has no vibration rating to mount anything that might vibrate (or be vibrated by the environment - the cause or source of vibration doesn't matter, KG of mass with a distant center of gravity shaking or being shook is all that matters).