Is the Hadith: "They are your Paradise and your Hellfire" weak, and what is the ruling on narrating it without disclosing its weakness, if it is weak?

The aforementioned Hadith (definition) is weak. Some scholars have permitted the narration of a weak Hadith concerning virtuous deeds, provided certain conditions are met: that it be narrated using a passive voice (such as: "it was narrated" or "it reached us"); that it pertains to virtuous deeds and the like, not to matters of creed or rulings; that its weakness is not severe; that it falls under a generally accepted principle; and that when acting upon it, one does not believe in its definitive authenticity, but rather exercises caution.