If I had to guess, the duration of Anthem of Weariness would not lengthen and neither would seconds of weakness either on your party. The only place where it may apply is strictly on yourself, afterall, you're wearing the heavy spear.
It should only lengthen the duration of weakness you apply, since each individual party member is causing weakness with their attack skills, not yours.
The only way to increase the duration of the anthem on the party is with skills, namely [[Vocal was Sogolon] or [[Enduring Harmony]. Equipment use has no effect on [[Anthem of Weariness]'s duration.
The condition duration question has already been answered.
