There are some comments out there claiming Vergil doesn't care for Nero, or perhaps only cares about his power. But I believe the final scene implies otherwise:
So when both Dante and Vergil agree to leave to cut the roots of the Qliphoth, Nero keeps catching up with them. Nero just learned he has a family, and just spend all his energy trying to save both of them. So he is stressing hard. Because after a brief moment, they're leaving again, and he's basically losing his new found family. Which is why he keeps running after them and trying to stop them.
So when Dante turns around to talk to him, he addresses the issue he thinks Nero has, which is being scared of being the 'Dead Weight'. Because that's been the repeating issue between them so far. So he tries to reassure him that he trusts him with 'things on this side', and that he can handle this on his own.
But the point is that's not what Nero needs to hear. It doesn't calm him down (you can clearly tell by how puzzled he looks and still runs after them after that). For the first time that's not the issue he's directly worried about at the moment, because he just proved his strenght in battle. He succeeded in saving them of eachother.
So when Vergil calls out to "Make Haste Dante", Dante leaves. If Vergil was in such a hurry, he would have jumped first. But he doesn't. He waits for Dante to leave, while he keeps his eyes on Nero, and I believe he pulled Dante away from Nero on purpose because he noticed his panic, and/or wanted to talk to him alone.
So left with Nero alone, he says 2 things. "I won't lose next time", implying that there will be a reunion, aka,' I will come back to you'. And the second, he asks him to hold onto his poetry book, as a physical reminder of that fact. The significance of Vergil entrusting the book to Nero has been analysed a lot so I won't delve into it, but obviously he gives Nero something that's very important to him. (In VoV it's described as his heart). And then he leaves.
The point is, Vergil noticed what Nero needed to hear. At that moment he didn't need to hear anything about strength or power or being good enough. He didn't need validation about not being the dead weight. All he needed to know was if his new found family would come back. And Vergil reassures him of that.
Which confirms to me he does care enough to do so for Nero, and also isn't completely unaware of his son's feelings. And that action just speaks volumes to me.
