Centering it and tightening the nut won't work. That's because the brake and fork already have a preferred position that they've carved into each other. You can't see the notches because they so small.

Whack one spring, as described above. Most of the time, this doesn't weaken the spring; it rotates the whole caliper, allowing new tiny notches. And if it does weaken the spring, that's ok, too.

Do oil the spring where it meets the arms.

Sidepulls are really an excellent design. Once you get the hang of it, they're easy to maintain.

Most of the techniques above won't work. You can't loosen the nut and reposition and tighten the nut.