  We answer a question raised by Pillay, that is whether the infinite weight of
the generic type of the free group is witnessed in $F_{\omega}$. We also prove
that the set of primitive elements in finite rank free groups is not uniformly
definable. As a corollary, we observe that the generic type over the empty set
is not isolated. Finally, we show that uncountable free groups are not
$\aleph_1$-homogeneous.
