Consider a finite data set of price vectors and consumption bundles; under what conditions will be there a weakly separable utility function that rationalizes the data? This paper shows that rationalization in this sense is possible if and only if there exists a preference order on some finite set of consumption bundles that is consistent with the observations and that is weakly separable. Since there can only be a finite number of preference orders on this set, the problem of rationalization with a weakly separable utility function is solvable