Short description of error
Only the active vertex group is copied to the destination mesh.
The manual states "By default this tool copies all vertex groups contained in the selected objects to the target object."
Exact steps for others to reproduce the error
Selecting the source mesh, then shift-selecting the destination mesh, then selecting Weight-Paint, and then pressing Transfer Weights.
I tested this with matching empty groups on the destination, and with no groups on the destination.
It's easy to see that only the source's active group is copied.
There is no way to select multiple or all groups on the source.