Polyphone disambiguation is the most crucial task in Mandarin grapheme-to-phoneme (g2p) conversion. Previous studies have approached this problem using pre-trained language models, restricted output, and extra information from Part-Of-Speech (POS) tagging. Inspired by these strategies, we propose a novel approach, called g2pW, which adapts learnable softmax-weights to condition the outputs of BERT with the polyphonic character of interest and its POS tagging. Rather than using the hard mask as in previous works, our experiments show that learning a soft-weighting function for the candidate phonemes benefits performance. In addition, our proposed g2pW does not require extra pre-trained POS tagging models while using POS tags as auxiliary features since we train the POS tagging model simultaneously with the unified encoder. Experimental results show that our g2pW outperforms existing methods on the public CPP dataset. All codes, model weights, and a user-friendly package are publicly available.