Brake Pivot Bolts
I can't say for certian without seeing the brakes, but I imagine your old Weinmann calipers have "nutted" pivot bolts, ie they are longer and secured to the frame with nuts, whereas your more modern brakes use "recessed" Allen Key nuts which go into the frame itself.
I've got round this problem in the past when using Campagnolo SR Calipers by fitting the front caliper to the rear and changing the too short rear bolt to a replacement front "nutted" bolt (hopefully that makes sense!).
I'm not sure though that you would be able to get a replacement "nutted" pivot bolt for your modern dual pivot brakes, someone else may be able to advise on that.
The only other option I believe is to drill out the rear of each brake mounting hole on your frame to take the new recessed nuts. This is not too bad on the forks as you can remove them to make access easier, but the closeness of the seat tube makes drilling out the rear more awakward.