In Sharia, we are not allowed to use weak hadiths to derive Fiqh and Ahkahm rules.
Only Sahih(Authentic) and Good(Hasan) hadiths can be used for that. Thus, any Hadith:
Weak (not fabricated nor really weak).
Never makes something halal nor haram.
Never think that the hadith is sunnah of the prophet.
There exist another verse or/and hadith which back(s) it up.
Only enjoin good and forbid bad deeds (i.e: Be kind to parents, remembering allah when entering markets, etc..)
Such Hadiths fall under the criteria of Faza'il-e-A'maal (فضائل الاعمال).
For example, the hadith below is an example of weak hadith. However, There are verses in the Quran that back this hadith.
Ibn 'Abbas (May Allah be pleased with them) said:
The Messenger of Allah (ﷺ) said, "If anyone constantly seeks pardon (from Allah), Allah will appoint for him a way out of every distress and a relief from every anxiety, and will provide sustenance for him from where he expects not."
[Abu Dawud - Sunnah.com]
The veses that backs this hadith:
http://quran.com/71/9-12, this http://quran.com/11/3, and this
Note: There is a book called Faza'il-e-A'maal. Check Ansari's answer for more information.
Please don't confuse between these two. One is a book and the other one is a concept