Heterogeneity of human beings leads to think and react differently to social phenomena. Awareness and homophily drive people to weigh interactions in social multiplex networks, influencing a potential contagion effect. To quantify the impact of heterogeneity on spreading dynamics, we propose a model of coevolution of social contagion and awareness, through the introduction of statistical estimators, in a weighted multiplex network. Multiplexity of networked individuals may trigger propagation enough to produce effects among vulnerable subjects experiencing distress, mental disorder, which represent some of the strongest predictors of suicidal behaviours. The exposure to suicide is emotionally harmful, since talking about it may give support or inadvertently promote it. To disclose the complex effect of the overlapping awareness on suicidal ideation spreading among disordered people, we also introduce a data-driven approach by integrating different types of data. Our modelling approach unveils the relationship between distress and mental disorders propagation and suicidal ideation spreading, shedding light on the role of awareness in a social network for suicide prevention. The proposed model is able to quantify the impact of overlapping awareness on suicidal ideation spreading and our findings demonstrate that it plays a dual role on contagion, either reinforcing or delaying the contagion outbreak.