Backchannels, which signal listener states like empathy and understanding, are fundamental to natural human interaction. However, current approaches rely solely on audio and text. This omits crucial visual cues, such as facial expressions and gestures, as well as broader conversational contexts, which are necessary for accurate prediction. In this paper, we introduce Context-Aware Multimodal Alignment for Backchannel Prediction (CAMA-BC), a novel framework that leverages visual information through Multi-layer Multimodal Alignment (MMA). Our alignment process comprises two stages. First, Context Alignment (MMA-CA) utilizes unlabeled dialogues with videos to capture conversational contexts. Next, Backchannel Alignment (MMA-BA) fine-tunes the representations specifically for backchannel prediction. Experimental results show that CAMA-BC significantly outperforms both existing methods and simple multimodal baselines, with particular effectiveness in recognizing complex backchannels such as empathy.