I couldn't really see anything but fuzzy might mean a mealy bug ot cottony scale. Hope that isn't the case. I just had that problem for the past two years and I think it is finally gone. Finally.
What you are seeing is actually a good thing - those are the eggs of a lacewing fly, which are laid at the ends of stiff silk threads. The larvae, when they hatch, are voracious predators on such pests as aphids. Nice to have around. Look up lacewing on bugguide.com if you want to know more.
Dave