When reviewing previous runs I found that the variable displayed as applied weight was some other variable than my "WEIGHT_final". In fact, it mentioned some var that wasn't in the Demographics file at all (anymore), e.g.:
Filters & Weights
Included Tasks: Task3,Task4,Task5,Task6,Task7,Task8,Task9,Task10,Task11,Task12
Respondent filters: None
Respondent weighting variable: Att2_payin.2_2
At one point it actually said the applied weight was "CHOICE", i.e., my dependent variable. This is just a bug in displaying I suppose?