Common misconception that weak hadith have no application at all. We do not use the weak for doctrine or law, but we do act upon them in extra deeds related to dua, manners, etc. And we may relay stories that are weak, provided no doctrine or law is involved. Furthermore, not all weak hadiths are the same. There are five conditions for a hadith to be sahih. Missing only one makes it weak. But missing two would make it weaker. Missing three and it's very weak. Missing four and its threadbare. The absence of multiple links in the chain is greater than missing only one name in the chain. So when you hear the word "da'if" you have to ask, how da'if? Lastly, there's another factor. Is the weak hadith repeated elsewhere? Multiple weak hadiths of the same meaning could be elevated to hasan. We still won't use it for doctrine or law but will have more basis to use it for other good actions.