I'm guessing the problem is either your pads and/or pad adjustment. First how old/worn are your brake pads; with 6510's they could be over 10 years old. If you haven't replaced your pads for a number of years it would be a good idea to start with that. Next, take a close look at your pads and see that the surface of the pads is even with the rim surface. Even though the pad may be adjusted so it looks like it's contacting the right area of the braking surface, the pad may be canted at an angle so just the top or bottom edge of the pad is contacting the surface. IOW, there is a flat surface on the rim and a flat surface to the brake pads, make sure these two surfaces meet as flush as possible. This will not normally happen with the standard pad setup; ie, being loosen the pads, compress the brakes and tighten the pads. You will need to loosen the pad, line up the brake and then raise or lower the bolt in the brake arm, while keeping the brake pad still lined up on the rim, until flat meets flat. This may take some trial and error until you get it right. Dual pivot brakes work well when they adjusted very close to the rim. Try and adjust the brakes so they start to grab hard at 50% of the travel.