Massive activations, which manifest in specific feature dimensions of hidden states, introduce a significant bias in large language models (LLMs), leading to an overemphasis on the corresponding token. In this paper, we identify that massive activations originate not from the hidden state but from the intermediate state of a feed-forward network module in an early layer. Expanding on the previous observation that massive activations occur only in specific feature dimensions, we dive deep into the weights that cause massive activations. Specifically, we define top-$k$ massive weights as the weights that contribute to the dimensions with the top-$k$ magnitudes in the intermediate state. When these massive weights are set to zero, the functionality of LLMs is entirely disrupted. However, when all weights except for massive weights are set to zero, it results in a relatively minor performance drop, even though a much larger number of weights are set to zero. This implies that during the pre-training process, learning is dominantly focused on massive weights. Building on this observation, we propose a simple plug-and-play method called MacDrop (massive weights curriculum dropout), to rely less on massive weights during parameter-efficient fine-tuning. This method applies dropout to the pre-trained massive weights, starting with a high dropout probability and gradually decreasing it as fine-tuning progresses. Through various experiments, including zero-shot downstream tasks, long-context tasks, and ablation studies, we demonstrate that \texttt{MacDrop} generally improves performance and strengthens robustness.