By giving Levi the syringe, he could hope that Levi would use it in some unforeseen way to aid his cause. He also likely felt some guilt at having all his comrades die in his attempt to gain the power of the Founding Titan.
At the brink of death, Kenny confesses that he is Levi's uncle, explaining that he left Levi because Kenny viewed himself not fit to be a father. As a final gift, Kenny gives Levi the Titan injection that he stole from Rod.
Kenny admitted that Levi was his pride and joy, though to someone who was about to die. It was possibly something he'd never admit out loud or to anyone, it just wasn't his style, so he confessed it to someone he was about to murder (lmao).
When Levi was first introduced, he was one of the most mysterious characters in the series, with people not even knowing what his last name was. However, after Kenny revealed to him that he was his uncle in his final moments, Levi found out that he was an Ackerman.
So according to the man himself, Levi did feel sadness and a sense of loss at the death of Kenny. Learning Kenny's identity, that he was his uncle and not his father, gave Levi relief. The question “who are you and what were you to my mother?” was something that had troubled Levi his entire life.
In Levi's eyes there is a great sadness following Hange's sacrifice. Unlike the others, he does not watch Hange's death but quietly sits and says “See you” to Hange, and asks them to watch him and the others.
Long after the persecution of the Ackerman clan, Kuchel took to working in a brothel in the Underground. She ended up being impregnated by one of her clients. Her elder brother Kenny Ackerman eventually found her, and unsuccessfully tried convincing her not to keep the child.
Kenny Ackerman
If it weren't for Kenny, Levi would never have been strong, but that strength was eventually used against him. While Levi joined the Survey Corps, Kenny became the captain of the Anti-Personnel Control Squad. These two groups in the military ended up fighting against each other.
These two lines together heavily suggest that Levi didn't know he was an Ackermann until the Interior MP mentioned Kenny's last name, and even then, only because he suspected that Kenny was his father.
Kenny's main goal was to obtain power, and his personality was molded around this goal. As such, he was a ruthless, sarcastic and manipulative individual who did not hesitate to do anything to get the job done, including a murderer or a traitor.
While there are many characters that he respects, Erwin Smith is perhaps the only character that Captain Levi has truly loved, which puts Erwin at the very top of the list. Levi's loyalty and devotion to Erwin also indicate that the two were meant to be together.
In the 進撃の巨人 ANSWERS/Shingeki no Kyojin ANSWERS Guidebook, Hajime Isayama, the writer of the series, states that Kenny was attracted to Uri.
Rod Reiss - Though Kenny initially seemed loyal to Rod, acting as a sort of 'right-hand man' for him, he lacked any respect for the true King of the Walls. He saw Rod as a self-serving coward, incomparable to Uri at least, and only obeyed him to fulfill his dream of inheriting the Founding Titan.
Although Grisha hated himself for it, he did it in order to fulfill Eren's wishes, and it's here that puts the whole series in a new context. Essentially, Eren drove Grisha to attack Frieda and steal the power of the Founding Titan in order to eventually make sure it's passed onto him.
Hoping he will lead her to the real king of the Walls, Annie decides to follow him. When Kenny discovers and confronts her about it, Annie attempts to deceive him by telling him that she is his long-lost daughter. Unsuccessful in fooling him, Annie attacks Kenny and flees into the sewers.
At that moment, Kenny decided to leave him behind, satisfied that he had taught Levi the skills he needed to survive. Later, he became a notorious thug in the underground but eventually left the place to join the Survey Corps. Although he was at odds with Erwin, he ended up becoming one of his most trusted men.
In 1977 at the age of 58, Levi retired as a part-time consultant at the SIVA paint factory to devote himself full-time to writing.
Mike speaks of his faith in humanity to Nanaba. Mike Zacharias (ミケ・ザカリアス Mike Zakariasu?) was the squad leader (分隊長 Bun-taichō?) of Squad Mike, a major division of the Survey Corps. A trusted soldier, he was considered humanity's second strongest soldier after Captain Levi.
Before Levi joined the Survey Corps, Mike was known as humanity's strongest soldier. He had strange habits, such as smelling people that he first meets. Despite his quirks, he was incredibly powerful and faced every challenge that came his way.
Levi was Petra's captain and Petra his subordinate. The two had their first encounter when the newly formed Special Operations Squad held their first meeting after Levi personally handpicked Petra as one of his members.
Kuchel Ackermann (クシェル・アッカーマン Kusheru Akkāman?) was the younger sister of Kenny Ackermann and the mother of Levi Ackermann. She worked as a prostitute in the Underground.
Kenny is with Levi 4 years (I can't imagine it's any longer) Once Levi is old enough to murder an adult man take care of himself, Kenny abandons him. Levi looks to be 10? Interestingly, Eren and Mikasa killed adults at the age of 9.