If the thing has set for a long time with the belt under tension, the belt may have developed a spot where it goes around the pulley, (especially the small one) that doesn't want to straighten out easily. With the belt off, see if it seems to be flexible when you hang it from a finger. If there is a spot where it wants to hang egg shaped from your finger the rubber in the belt has taken the shape of the pulley and will make a noise every time that spot goes around the pulley. May work itself out, may need a new belt.
Alexis de Tocqueville was a very smart man.