The aim of this paper is to study the analysis of contingency tables with one heavyweight column or one heavyweight entry by taxicab correspondence analysis (TCA). Given that the mathematics of TCA is simpler than the mathematics of correspondence analysis (CA), the influence of one heavyweight column on the outputs of TCA is studied explicitly without recourse to asymptotics as done by Benzecri ("Les Cahiers de L'Analyse des Donnees" 4:413-416, 1979). A reweighting of the heavyweight column is proposed, which can also be applied to CA. A real data set is analyzed.