I know this is an ancient thread but I stumbled across it looking for info on a specific Weinmann lever and thought I might chip in on the off chance that someone else wants to know how to adjust a Weinmann brake with a plastic cap.
Overview, attachment and centering
Contrary to web opinion, these brakes are not crap. The braking arms rotate around a steel shaft aligned with the centre of the bike, meaning that both sides travel the same arc to reach the (presumably central) rim. The arms are pulled away from the rim by a spring which is anchored on the shaft, the ends of the spring protruding on each side and engaging on a tab on each arm. The shaft is attached to the frame (either fork crown or rear bridge) by either a nyloc nut (i.e. one with a nylon insert to discourage it from working its way loose) or (in the fancy versions) a fancy Allen cap screw - an alternative to the nyloc nut that gives you that cool aerodynamic effect of which we are all so fond. Either way, tightening this back nut to fix the brake to the bike has a tendency to rotate the shaft and move the spring so the force applied to one arm is greater than the other. When this happens, one brake block may sit closer to the rim than the other in the neutral (not braking) position, even touching the rim if the spring is moved enough.
Weinmann was not daft. The designers figured that if the mechanic could control the rotation of the shaft when the back nut is tightened then there would be complete control over the neutral position, so they designed in a hexagonal head to the non-fastened end of the shaft and a tool (basically a small socket) that fits on it. Thus when you tighten the nut, you waggle the tool (technical process) to set the position of the spring.
Right. Point 2. Washers
There should be thin brass washers between the arms and the surrounding bits of the mechanism - and one between the arms. These exist to stop the arms binding against each other when the mechanism operates. There is normally a standard thickness washer next to the securing nut to further ease the securing of the shaft to the bike. If you have a mudguard or carrier support that needs to be included, the washer goes outside this - i.e. remains next to the nut. There should NOT be a washer between the spring carrier and the frame. Put one here and you will have no end of problems trying to persuade the spring to centre. The idea is that the spring carrier remains in a fixed position relative to the frame.
Finally, point 3. "Unwanted rocky back and forth motion".
When you pull off the stylish black cap, you will find 2 thin nuts on the end of the shaft. If you wind the inner one in towards the arms, eventually the arms bind and won't retract. This is too tight and a bad idea. Wind the nut back (with the skinny spanner Weinmann made for the job) until the arms move without binding. Now tighten the other nut against the 1st so that everyday vibrations don't shake the nuts off the shaft (also bad). There is a tendency for the act of locking the nuts together to wind the nut closer to the arm away from it, reintroducing unwanted rocky back and forth motion - so you need to test the clearance after the nuts are locked and if necessary adjust. Push the stylish black plastic cover back over the lock nuts and admire your work. I'm not going to tell you how to line up your brake blocks with the rim because if you find this task in any way daunting, then you should ignore all the above and take your bike to a professional in any case. If they tell you to fit new brakes, move to the next one.
Hope this helps, although it is clearly too late to keep Weinmann and their well-designed, spares-supported, effective brakes in business. Ah well.
Z
PS/ In the olden days we used to use a special lever (pretty much a spanner whose open end fit over the arm at the brake block mounting face with its shaft pointed laterally out) to bend the arms ever so slightly (a couple of degrees ish) to ensure that the leading edge of the brake block contacted the rim first. This improves feel and discourages the vibrations that get called "judder" and "squeal". Weinmanns (and steel callipers) were quite tolerant to this kind of abuse. CLBs had an irritating tendency to snap. Guess this is the difference in the alloy used.