Researchers cite works for a variety of reasons, including some having nothing to do with acknowledging influence. The distribution of different citation types in the literature, and which papers attract which types, is poorly understood. We investigate high-influence and low-influence citations and the mechanisms producing them using 17,154 ground-truth citation types provided via survey by 9,380 authors systematically sampled across academic fields. Overall, 54% of citations denote little-to-no influence and these citations are concentrated among low status (lightly cited) papers. In contrast, high-influence citations are concentrated among high status (highly cited) papers through a number of steps that resemble a pipeline. Authors discover highly cited papers earlier in their projects, more often through social contacts, and read them more closely. Papers' status, above and beyond any quality differences, directly helps determine their pipeline: experimentally revealing or hiding citation counts during the survey shows that low counts cause lowered perceptions of quality. Accounting for citation types thus reveals a "double status effect": in addition to affecting how often a work is cited, status affects how meaningfully it is cited. Consequently, highly cited papers are even more influential than their raw citation counts suggest.