Hello,
The WL option can be used to fit weighted histogram, representing sum of weighted counts, i.e. in case you gave a Poisson process giving {w_i} counts in each bin.
You can find a theoretical explanations in this paper, https://arxiv.org/pdf/1309.1287.pdf
ROOT implements what is described in paragraph 3: the approximation with a scaled Poisson distribution.
In your case, it seems to me you have an histogram where the bin content follows a particular model. If the error is computed from error propagation, you are basically using a Normal approximation. I think in this case it would be more appropriate doing a standard least-square fit, the default in ROOT and not use option “WL”.
Best regards
Lorenzo