Post #2579: 
anphung:
What keymap/ context should I use for modifier popup?
What code and where you use it for the modifier popup? Afaik you can use any keymap for it.
anphung:
How do I add this (Weight) to a menu?
You can find modifier by its name (Property tab):
C.object.modifiers["Weighted Normal"].weight
Or by its type (Property tab):
find_by(C.object.modifiers, "type", 'WEIGHTED_NORMAL').weight