Because of the inherent weigthing effect of the two dimensional fit it was decided not to use the typical intensity weighted fit, but allow the Downhill Simplex method to weight all datapoints according to their combined quality to fit to the 2D Two disk model.
Intrinsically the use of a weighting based on the intensity means that the higher the intensity the lower the error. This because a higher brightness will be more accurately detected than a faint brightness. Intensity weighting does not allow for residual structures like unmasked faint stars, which show up as bright peaks in the background noise. These will influence the fit since they get weighted equally as points with the same intensity, giving systematical errors to the fit instead of the normal statistical errors.
Even though using a quadrasized average image minimalizes these peaks there is still a chance that such a false datapoint remains, especially when one side of the residual background has a brighter structure than the other side. For these issues doing a two dimensional fit with the Downhill Simplex method has another advantage over the slightly biased intensity weighting due to bright datapoints in the background noise. The Downhill Simplex method compares the values of each datapoint of each cut with each other. The thin disk component will show up clearly and smooth in each cut and thus will contribute strongly to the determination of its parameter values. The thick disk component however, will be less smooth and on larger radii the thick disk component will start losing signal because we use a surface brightness limit on the profile. The Downhill Simplex method searches for the best fit for all those cuts combined. If a datapoint is erratic and doesn't follow the two dimensional fitting function as well as the datapoints from the other cuts it will automatically contribute less to the fit and get a lower weighting, even if they have a higher intensity in the case of a bright peak in the background noise. This effect showed clearly during our fits.