This paper examines the topological mixing properties of n-tuples of operators on Fréchet spaces. The authors characterize when a pair of unilateral backward weighted shifts is topologically mixing in terms of limits of the weighted sequences. They show that a pair is topologically mixing if and only if the products of the weights along the sequences approach nonzero limits. Similarly, they characterize when a pair of bilateral backward weighted shifts is topologically mixing. The results apply the hypercyclicity criterion for syndetic sequences to prove topological mixing.