Dear all,
I posted the full question on StackOverflow and as it contains some figures I refer you to that post.
I currently believe that this issue is a bug and I opened an issue on GitHub.
To sum up, the issue is that GridSearchCV does not handle the splitting of the sample_weight vector during cross validation.
Nota bene: cross_val_score seems to handle the splitting OK, this issue seems to occurr only in GridSearchCV.
Any comments enlightening me and showing me how wrong I am are most welcome.