2 object occupying the same space with the exact same geometry. They both need to be influence by one bone identically. I edited one's paint weight so I want to have the same changes applied to the other.
I was suggested to:
Select the object with the correct weight(source)
Shift select the object that you want to copy weights.
In weight paint hit [ Transfer Weights ]
Opens the Transfer Mesh Data tab.
hit [ Transfer Weights ] again.
I tested it in pose mode but it didn't work they are still different.
Upon additional information
Hit [ Transfer Weights]
For Source Layer destination select: By Name
For Destination Layers Matching select: All layers
For Mix Mode select: Replace