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A weighing matrix \(A = A(n, k)\) of order \(n\) and weight \(k\) is a square matrix of order \(n\), with entries \(0, \pm1\) which satisfies \(AA^T = kI_n\). H.C. Chan, C.A. Rodger, and J. Seberry “On inequivalent weighing matrices, \({Ars \; Combinatoria}\), \((1986) 21-A, 299-333\)” showed that there were exactly \(5\) inequivalent weighing matrices of order \(12\) and weight \(4\) and exactly \(2\) inequivalent matrices of weight \(5\). They showed that the weighing matrices of order \(12\) and weights \(2, 3\), and \(11\) were unique. Q.M. Husain “On the totality of the solutions for the symmetric block designs: \(\lambda = 2, k = 5\) or \(6\),” Sanky\(\bar{a}\) \(7 (1945), 204-208\)” had shown that the Hadamard matrix of order \(12\) (the weighing matrix of weight \(12\)) is unique. In this paper, we complete the classification of weighing matrices of order \(12\) by showing that there are seven inequivalent matrices of weight \(6\), three of weight \(7\), six of weight \(8\), four of weight \(9\), and four of weight \(10\). These results have considerable implications for inequivalence results for orders greater than 12.