The solution here is to use untf=TRUE for abline param when you are using the log="xy" scale.
If untf is true, and one or both axes are log-transformed, then a curve is drawn corresponding to a line in original coordinates, otherwise a line is drawn in the transformed coordinate system. The h and v parameters always refer to original coordinates.
plot(log.Weight~log.Width,data=DF,log="xy")
abline(FIT,col="blue",untf = TRUE)