Note that h->Sumw2(kFALSE); completely destroys the existing “weights”. The following “Fit” will usually be meaningless.
If you read the TH1 Class Reference, you will (in many places) find the opposite advice (i.e. you should execute h->Sumw2(kTRUE);)
IMPORTANT NOTE: If you intend to use the errors of this histogram later you should call Sumw2 before making this operation. This is particularly important if you fit the histogram after …
The HIST option tells the histogram to be drawn only … not the function. That’s why the fit (which is a function) is not drawn. I would suggest to make a copy of the original histogram, on which you call Sumw2. Like that you do not destroy the original histogram, if you want to use the errors later on.