The loglog plot is similar to the classic weibull scales plotted when using ProbabilityScalePlot, yet isn't the same. For the CDF the vertical scale should go from near zero to near 100% (or 1 by some authors)
When using just, ProbabilityScalePlot[data, "Weibull"]
from your example - the scales loo right.
And, I'm pretty sure that I can update the output to include labels, classic grid lines, etc.
The problem is that I've not been able to find a way to plot the 'straight line' representing the known distribution on the weibull probability paper scales, without having to use RandomVariate and fit a line. If that is the only way to get to the probability scaled paper, then, is it possible to plot only the fitted line or reference and not the data points?
In my case, I have the weibull parameters, and not the data.
It's one of those problems that should be easy....