In mass media, the positions of science deniers and scientific-consensus advocates are repeatedly presented in a balanced manner. This false balance increases the spread of misinformation under the guise of objectivity. Weight-of-evidence strategies are an alternative, in which journalists lend weight to each position that is equivalent to the amount of evidence that supports the position. In public discussions, journalists can invite more advocates of scientific consensuses than science deniers (outnumbering) or they can employ warnings about the false-balance effect prior to the discussions (forewarning). In three pre-registered laboratory experiments, we tested the efficacy of outnumbering and forewarning as weight-of-evidence strategies to mitigate science deniers' influence on individuals' attitudes towards vaccination and their intention to vaccinate. We explored whether advocates' responses to science deniers (rebuttal) and audiences' issue involvement moderate the efficacy of these strategies. A total of N = 887 individuals indicated their attitudes towards vaccination and their intention to vaccinate before and after watching a television (TV) discussion. The presence and absence of forewarning, outnumbering and rebuttal were manipulated between subjects; participants also indicated their individual issue involvement. We obtained no evidence that outnumbering mitigates damage from denialism, even when advocates served as multiple sources. However, forewarning about the false-balance effect mitigated deniers' negative effects. Moreover, the protective effect was independent of rebuttal and issue involvement. Thus, forewarnings can serve as an effective, economic and theory-driven strategy to counter science denialism in public discussions, at least for highly educated individuals such as university students.