Event-by-event weighting and saving as a branch at TTree

Yes, I fully agree that this doesn’t make any sense.

I just tried to follow the previous topic about similar question (TTree Weighting is different from TH1 weighting), where one of the final responses was:
" I believe the standard way is to add a weight branch with the weight. You can do the multiplication later: the information will be fully available in the tree."

So now I am trying how it should be done.

Thanks for your help.