Visual information extraction (VIE) has attracted increasing attention in recent years. The existing methods usually first organized optical character recognition (OCR) results into plain texts and then utilized token-level entity annotations as supervision to train a sequence tagging model. However, it expends great annotation costs and may be exposed to label confusion, and the OCR errors will also significantly affect the final performance. In this paper, we propose a unified weakly-supervised learning framework called TCPN (Tag, Copy or Predict Network), which introduces 1) an efficient encoder to simultaneously model the semantic and layout information in 2D OCR results; 2) a weakly-supervised training strategy that utilizes only key information sequences as supervision; and 3) a flexible and switchable decoder which contains two inference modes: one (Copy or Predict Mode) is to output key information sequences of different categories by copying a token from the input or predicting one in each time step, and the other (Tag Mode) is to directly tag the input sequence in a single forward pass. Our method shows new state-of-the-art performance on several public benchmarks, which fully proves its effectiveness.