  We study supersymmetric Wilson loops in the ${\cal N} = 6$ supersymmetric
$U(N_1)_k\times U(N_2)_{-k}$ Chern-Simons-matter (CSM) theory, the ABJ theory,
at finite $N_1$, $N_2$ and $k$. This generalizes our previous study on the ABJ
partition function. First computing the Wilson loops in the $U(N_1) \times
U(N_2)$ lens space matrix model exactly, we perform an analytic continuation,
$N_2$ to $-N_2$, to obtain the Wilson loops in the ABJ theory that is given in
terms of a formal series and only valid in perturbation theory. Via a
Sommerfeld-Watson type transform, we provide a nonperturbative completion that
renders the formal series well-defined at all couplings. This is given by ${\rm
min}(N_1,N_2)$-dimensional integrals that generalize the "mirror description"
of the partition function of the ABJM theory. Using our results, we find the
maps between the Wilson loops in the original and Seiberg dual theories and
prove the duality. In our approach we can explicitly see how the perturbative
and nonperturbative contributions to the Wilson loops are exchanged under the
duality. The duality maps are further supported by a heuristic yet very useful
argument based on the brane configuration as well as an alternative derivation
based on that of Kapustin and Willett.
