I'm not familiar with the details of Grafit. However, to know whether
the problem is due to a fault in the software or with the data or the
way you have entered them, one really needs a numerical example. Can
you provide a set of data with the parameter values that you get, both
from the software and from your plots? It's not necessary to have a
complete set of data with many observations, as long as the abridged
data display the same peculiarities as you get with the complete set.
My book "Analysis of Enzyme Kinetic Data" (Oxford University Press,
1995; http://ir2lcb.cnrs-mrs.fr/lcbpage/athel/leonora.html) discusses
many points related to the sort of problem you have.
Athel Cornish-Bowden