The super Catalan numbers T(m,n)=(2m)!(2n)!/2m!n!(m+n)! are integers that generalize the Catalan numbers. With the exception of a few values of m, no combinatorial interpretation is known for T(m,n). We give a weighted interpretation for T(m,n) and develop a technique that converts this weighted interpretation into a conventional combinatorial interpretation in the case m = 2.