End-to-end (E2E) automatic speech recognition (ASR) models have become standard practice for various commercial applications. However, in real-world scenarios, the long-tailed nature of word distribution often leads E2E ASR models to perform well on common words but fall short in recognizing uncommon ones. Recently, the notion of a contextual adapter (CA) was proposed to infuse external knowledge represented by a context word list into E2E ASR models. Although CA can improve recognition performance on rare words, two crucial data imbalance problems remain. First, when using low-frequency words as context words during training, since these words rarely occur in the utterance, CA becomes prone to overfit on attending to the <no-context> token due to higher-frequency words not being present in the context list. Second, the long-tailed distribution within the context list itself still causes the model to perform poorly on low-frequency context words. In light of this, we explore in-depth the impact of altering the context list to have words with different frequency distributions on model performance, and meanwhile extend CA with a simple yet effective context-balanced learning objective. A series of experiments conducted on the AISHELL-1 benchmark dataset suggests that using all vocabulary words from the training corpus as the context list and pairing them with our balanced objective yields the best performance, demonstrating a significant reduction in character error rate (CER) by up to 1.21% and a more pronounced 9.44% reduction in the error rate of zero-shot words.