We were able to figure out the meaning of almost all of the road signs eventually, but these signs stumped us. And they were everywhere.
They can't be a speed limit, because the speed limit signs were very different, and were very clear and unmistakable. And besides, these often appeared on roads next to the speed limit signs and they gave different numbers.
It was suggested by someone to me that they are a weight limit. However, I can't imagine what unit of measurement they're in, or why it would give two different values. Besides, we saw and sussed the weight limit signs, and those were completely different and were much more clear. The weight limit signs were a red circle with the limit in tons in the middle of the circle (such as '3,5t', meaning weight limit 3.5 metric tons). So this clearly isn't the same thing as the weight limit signs.
A final clue is that these sometimes had little icons of trucks and/or tanks on them. Which would lend credence to the weight limit theory, but I still can't figure out the reason for the two values, or what the unit of measurement is.
It really puzzled us, so if anyone from Germany knows what these mean, drop me a line.
Edit: Rob S. got me on the right track by telling me they were for military use only. According to this page, they indicate bridge carrying capacity for NATO vehicles. I don't know what the unit of measurement is, I guess it has to be metric tons.