Weak measurement and distinguishability

Suppose you can perform any weak measurement of your choice on an ensemble of particles composed of two equally sized sub-ensembles, but you can’t use any other source of information about which individual particles belong to which sub-ensemble. Is there any way to use the weak measurement itself to distinguish between the following two scenarios?

1. Both sub-ensembles have the same weak value of $ +frac{1}{2} $
2. One sub-ensemble has a weak value of +1 while the other has a weak value of 0