What you are describing is the issue of Paternalism in ethics, describe by Gerald Dworkin as “interference with a person’s liberty of action justified by reason referring exclusively to the welfare . . . of the person being coerced.”
Dworkin takes issue with Mill's fairly absolute prohibition on the interference with private autonomy on the the grounds that we do not always know what is best for us and that at times other may have more concern for our welfare than we do. As such Mill's conclusion that our attempts to judge on behalf of others will lead to worse consequences than them doing so for themselves, is flawed.
Mill does allow for what has been termed 'soft paternalism', where the person may not be aware of the consequences of their actions and we might be unable to communicate the consequences effectively enough to allow them to make their own choice, but such cases are difficult to find in public health.
James Childress goes further to say that in more complex cases of public health, the consequences of an individual being in poor health are not borne solely by that individual. There will be consequent effects on their utility as a member of society, the burden they place on others, the risk they pose to others (if intoxicated, for example). In utilitarianism, it is ethical for the state (or any other individual), therefore, to interfere with private autonomy to ensure that individual is in a better state of health.
Sarah Conley goes even further to argue that because we make irrational choices that subvert our own goals, even when viewing humans as Kantian 'ends in their own right' we might be justified in interfering with their autonomy when we can; a) draw a reasonable conclusion as to what those ends might be, b) rationally conclude that their current means will frustrate these ends, and c) fail to effectively communicate that conclusion.
Critics of such interventions often cite the harms to individual freedom, but in a truly utilitarian framework the proposer of the intervention would be considering the net harm anyway, and so limiting themselves to that extent. This would prevent someone from, say, physically assaulting someone in order to prevent them from smoking in private. In Childress's view, to satisfy these requirements, interventions must be (1) effective, (2) proportionate, (3) necessary, (4) the least infringement that remains effective, and (5) publicly justified.
Ultimately, we are a social species and an individual's behaviour is never free of consequences for the society around them some of which may be net harms, it is therefore both rational and reasonable to use what influence one has to bring about the behaviour in others that one thinks would avoid those harms.