in this article, the above mentioned narration isn't addressed..
This statement and addition "Anta Khalifati", even though weak, is mentioned during the Tabuk expedition when the Prophet (saw) left Ali (ra) in Madina to take care of the women and children - hence "you are my deputy" is said in that context i.e. Ali being in charge in Madina until the Prophet (saw) and the Muslim army returns from Tabuk. Note: In other occasions the Prophet (saw) appointed various other companions in charge of Madina when He would leave the city.
Anyways, from twelvershia.net why the report is weak:
"Finally, the last narration that includes the addition is the narration of Abu Balj Al-Wasiti. However, his narration, while appearing to be strong, includes a hidden defect. We find in Sharh Ilal Al-Tirmithi by Ibn Rajab (p.493) that Ahmad questioned the narration of Amr bin Maymoon from Ibn Abbas, perhaps since the former is much older than him. Then Ibn Rajab adds that Abdul Ghani Al-Hafith believed that Abu Balj made a mistake in the narration and meant to say Maymoon Abu Abdullah (who is weak) when he said Amr bin Maymoon. Ibn Rajab sees this opinion as a valid one."Besides this, there are also other additions in Hadith of Ghadir Khum (wali kul mumin baadi) and they are also weak:
From TwelverShia.net
"So, in conclusion, the addition can be found in the narrations of weak narrators, and only one strong Shi’ee narrator, Ja’afar bin Sulaiman Al-Dhuba’ee, and this conflicts with all the authentic narrations that do not include this addition, therefore the addition is weak."You can also read more about this here under section
Shia Argument #3.
https://youpuncturedtheark.wordpress.com/2016/04/14/the-ghadeer-khumm-event-as-understood-by-ahlelbayt-sahaba-ahlus-sunnah/