How weak is weak extent?

We show that the extent of a Tychonoff space of countable weak extent can be arbitrarily big. The extent of X is e(X)=sup{|F|: F⊂X is closed and discrete) while we(X)=min{τ: for every open cover U of X there is A⊂X such that |A|⩽τ and St(A,U)=X} is the weak extent of X (also called the star-Lindelöf number of X). Also we show that the extent of a normal space with countable weak extent is not greater than c.