Even if they fight sometimes, Jughead and Veronica are friends who hang out together in a group, and they play in the same band. He goes to her parties. He should show concern for her if she's crying. If he decides to ignore her because of what you said about her treating Archie badly, he is wrong to do that, just as Veronica would be wrong to ignore him because of his misogyny, if their positions were reversed.
I don't think his response in the last panel seemed weak or undecided. Jughead isn't the kind to say something unless he means it. I doubt Veronica bursts into tears because of what Reggie says; she was already crying. They are across the street, so she probably can't hear them. But I agree with how you described Jughead's motives and thoughts when he talks to Betty.I don't think that what Jughead said to Betty earlier is bad; I just think that he was wrong to make fun of Veronica for crying and not ask her why.