If you have a miner's bag (inside a container at least) and use it directly on ore that you have not yet picked up, the weight you are carrying does not increase.
I've also noticed that you don't always lose the weight when you dump the bag either, but I'm less sure of the exact circumstances that trigger that. For example, when I've emptied the bag directly into the smelter, it doesn't seem to lessen my carry weight immediately.
Both error conditions can be corrected by equipping armor or clothing. That is, the weight updates when the equip action is performed, so that's a work around.