You seem to use a modified Lev-Mar routine that you have not attached, so it is not clear what is going on. My best guess from the limited data is the following problem:
You wire an array of "1s" to the Stdev input, yet your Y data is in the range of 1e-4. This means that the fit is considered converged if it is within a stdev of 1. This is not good enough! Try replacing the diagram constant (near upper left corner in diagram) which is currenty "1" with e.g. "1E-6" and see if things improve. 🙂