It has been a primary concern in recent studies of vision and language tasks to design an effective attention mechanism dealing with interactions between the two modalities. The Transformer has recently been extended and applied to several bi-modal tasks, yielding promising results. For visual dialog, it becomes necessary to consider interactions between three or more inputs, i.e., an image, a question, and a dialog history, or even its individual dialog components. In this paper, we present a neural architecture named Light-weight Transformer for Many Inputs (LTMI) that can efficiently deal with all the interactions between multiple such inputs in visual dialog. It has a block structure similar to the Transformer and employs the same design of attention computation, whereas it has only a small number of parameters, yet has sufficient representational power for the purpose. Assuming a standard setting of visual dialog, a layer built upon the proposed attention block has less than one-tenth of parameters as compared with its counterpart, a natural Transformer extension. The experimental results on the VisDial datasets validate the effectiveness of the proposed approach, showing improvements of the best NDCG score on the VisDial v1.0 dataset from 57.59 to 60.92 with a single model, from 64.47 to 66.53 with ensemble models, and even to 74.88 with additional finetuning.