Sequence-to-sequence neural generation models have achieved promising performance on short text conversation tasks. However, they tend to generate generic/dull responses, leading to unsatisfying dialogue experience. We observe that in the conversation tasks, each query could have multiple responses, which forms a 1-to-n or m-to-n relationship in the view of the total corpus. The objective function used in standard sequence-to-sequence models will be dominated by loss terms with generic patterns. Inspired by this observation, we introduce a statistical re-weighting method that assigns different weights for the multiple responses of the same query, and trains the common neural generation model with the weights. Experimental results on a large Chinese dialogue corpus show that our method improves the acceptance rate of generated responses compared with several baseline models and significantly reduces the number of generated generic responses.