Emotion recognition in conversation (ERC) is an interdisciplinary field focused on identifying the emotional state of each utterance in a dialogue. However, existing ERC studies use fixed and single prompt templates, and the resulting utterance embeddings fail to adequately represent the subtle semantic differences between utterances. Additionally, there is an unclear relationship between the way utterances are expressed and their corresponding emotional states, which impacts the model inference and the quality of generation. ERC datasets are typically class-imbalanced, leading to imbalanced gradients when handling different emotion categories. To address these issues, we propose the gradient reweighting-based representation intervention and prompting framework (GRIP-ERC). GRIP-ERC consists of a representation extractor and an unbiased classifier. In the representation extractor, GRIP-ERC adds soft prompts in the hidden layer of the PLMs, which are composed of task-specific and instance-specific elements, allowing for a more complete representation of the semantic differences of utterances. Additionally, GRIP-ERC intervenes in hidden representations within the linear subspace spanned by a low-rank projection matrix to guiding model behavior during reasoning and improving the quality of generation. In the unbiased classifier, GRIP-ERC reweights the imbalanced gradient matrix on a per-class basis and uses a balance vector adaptively adjusted by historical accumulated gradients. Experimental results show that GRIP-ERC outperforms state-of-the-art methods on all three benchmark datasets, validating its effectiveness.