Anthony would never have anything to do with the business, especailly after what happened to his sister... Or would he? "Curse of the father" sort of thing, perhaps. Where the death of his sister draws him in the way the hit on Vito drew Michael in.
You already said it yourself.
I think Anthony had not much of a choice left. I think after the tragedy at the opera I don't think he wanted to have anything to do with that anymore.
Though I have to say, that Anthony might wind up as more of a Fredo, perhaps.
Although I agree that he somewhat portrayed himself as a softy, I don't think he was actually weak, and definitely not stupid.
