[R] Fit a distribution to an "ECDF"

[MyKenk]

I have a growth curve, which is essentially an ECDF:  Statistically,
it's F(x)...

> GrowthCurve
 [1] 0.06919932 0.24154761 0.42206402 0.61412408 0.72228295 0.79727292
0.86605315 0.91271120 0.98258397 1.00000000

I'd like to fit a Weibull Curve (then a LogLogistic) to this ECDF, and
have no clue how to go about doing it.  I'm relatively new to R
(obviously).

Thanks!