To add an outline to the area, just change the colour :
ggplot(df,aes(x = Time,y = Acres,fill=WUClass)) + geom_area( position = 'stack') + geom_area( position = 'stack', colour="black", show_guide=FALSE)
But to draw lines, do the following:
ggplot(df,aes(x = Time, y = Acres, fill=WUClass, group=WUClass)) + geom_area() + geom_line(aes(ymax=Acres), position="stack")

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