The fatal error was to set the weighting matrix with diagonal elements as the error.
There weights are 1/errors**2.
There is though some un-answered questions left.
The Jacobian used, is the direct derivative of the function.
It is not the chi2 derivative Jacobian.
task #7822(https://gna.org/task/index.php?7822): Implement user function to estimate R2eff and associated errors for exponential curve fitting.