Scenes with Will's father, Charles, that reveal the symptoms of his Alzheimer's disease, especially after the effects of ALZ-112 wear off.
What makes it more heartbreaking is the first scene where Charles is trying to cut his food with the handle of his fork instead of the tines, prompting Caesar to gently turn it around for him. Charles appears to be both confused and embarrassed by his odd behavior, where Will is left slowly realizing that his father's Alzheimer's may have returned, and Caesar seems so distressed at the realization that something is not right with Charles.
The death of Charles, who refuses to take ALZ-113, signalling to his son that it was perhaps time to let him go.
Arguably made worse by the fact that the scene is completely wordless.
Caesar being separated from Will for the first time at the primate shelter.
Caesar drawing his attic window on his prison wall as a yearning for home. Said window later becomes an Arc Symbol throughout the trilogy.
Later, Will returns to get Caesar, and Caesar acts like he's angry at him and refuses to go with him. In reality, he'd bonded with the other apes in the shelter and had a mass escape plan prepared, and he could not abandon them. When Will leaves, we see Caesar's expression showing his true feelings and just how tempting the prospect of going back with Will really was for him.
Caesar learning that his mother died and that he is virtually a freak of nature different from humans and other apes.
Caesar's Accidental Murder of Dodge. Dodge deserved it, but Caesar still didn't want it to happen and the look on his face after it happens screams "My God, What Have I Done?". He firmly goes out of his way to stop Rodney suffering the same fate, calming the other apes and leading Rodney gently and apologetically to a cage.
Buck's death. All he wanted was freedom, which Caesar gave him, and in return gives up his life to defend Caesar: just when he was so close to truly being free.
Due to the Downer Ending described in the Main section, the realization that Caesar will likely soon lose his adoptive father as well. Harsher in Hindsight as of Dawn, where Caesar revisits his old home and finds old videos of Will.
Franklin's death. He was one of the only people at the facility who actually cared about all the apes, yet he dies a slow and probably agonizing death alone in his apartment as the first victim of the plague.
The immediate aftermath of Caesar attacking Hunsiker to protect Charles. After Hunsiker's daughter comes out, Caesar realizes that he made a mistake, and goes over to hug Charles. The expressiveness on his face is just gut-wrenching, as seen at the top of this page.
Everything about the attic window that Caesar draws on the wall of his cell.
