There are a number of causes, and the OP needs to divide and conquer. Step one remove the wheel (or shoes) and flex the arms by squeezing from the sides, or lifting the yoke, (not using the lever) and see if the action is smooth and crisp. If not the problem is in the brake, if yes, it's elsewhere.

As I remember, Weinmann brakes allowed adjustment of the pivots (it's been dacades so forgive me if I'm wrong), so it's possible that one pivot is set too tight. Back off the bolt and retighten the locknut on the back. If the play isn't adjustable (like on canti's) then odds are the tube the arms ride on is a bit short and the bolt is compressing them slightly. Here the fix is to thin one arm, or washer slightly so the bolt bottoms on the tube before compressing the arm.

If the brake itself is fine, then possibly the shoe is hanging under the rim by a lip that forms with wear. On my commuter, the first indicator of brake shoe wear is that the brake stays on after I stop, and releases the moment I move. Otherwise look at the cable, which is the most common cause of poor rear braking.