Weak ahadith are still valid ahadith
Just something I want to clear up.
A hadith with a weak chain of narration is still a valid hadith. It is not rejected or found to be manufactured - those have different terms for them.
The best example in this is one of parents. If a parent goes weak will you disown them? no.
In the same way, you cant disown a hadith simply because its chain of narration is weak. The historical position is that they are used for guidance and benefits, but not for rules.
PS a weak hadith can rise to a stronger position even as far as hasan if there are other similar ahadith that support its position.
Disclaimer: I am not a scholar.