Recently, Reddy and Pradeep (2023) have proposed a class of parameter choice strategies to choose the regularization parameter for the finite dimensional weighted Tikhonov regularization scheme. In this article, we explore the iterated weighted Tikhonov scheme in the finite dimensional context, discuss its convergence analysis and propose a class of parameter choice strategies to choose the regularization parameter. Furthermore we establish optimal rate of convergence as Oδj(α+1)j(α+1)+1 based on the proposed strategies. The scheme’s performance is illustrated through numerical experiments with an efficient finite dimensional approximation of an operator.