In Sweet Smell of Success (1957), J.J talking to his sister Susan and Steve Dallas, who is in love with J.J's sister Susan:
J.J: Steve wouldn't be much of a man if he didn't understand my concern, would you?
Steve Dallas: No, I wouldn't.
J.J: Serious as a deacon. I like it. I like it fine. In a world of old rags and bones, I like it.
What does "would you" mean? I feel his question is incomplete. Does it mean would you be a man?
This is a perfectly normal way to ask a question and there are a couple of reasons why people do this.
You are correct that it refers back to the point about 'being a man', and there is no need to repeat this in order to ask the question.
One reason for constructing a question this way is for additional politeness, for example, "you wouldn't happen to know, would you?"
In your example, the question is rhetorical. Sometimes rhetorical questions are defined as those which do not require or demand an answer. Of course, in your example an answer is given, but really the speaker was inviting someone to agree with them, and the answer was just that agreement. In this case, it sounds like the question was a little passive-agressive in tone, and the agreement was a forced hand. This form of question is not always in this spirit however, and like any rhetorical question can be used to reinforce a genuine point.
The speaker is speaking to two people. In the comment directed ostensibly to Susan, The speaker mentions Steve in the third person. but immediately shifts the question to directly address Steve, as if he had said
"You wouldn't be much of a man, would you?"
It is a rhetorical question for Steve, intended to influence him by threatening to shame him.
