This looks like bad writing. . . . or maybe good writing showing that the character speaking is not well educated (COULD OF should be COULD HAVE). In any case, 'six cents worth' doesn't have any particular connotation that I know of, so yes, it's probably similar to 'two cents worth.'

"Not six cents worth" means the person didn't give any information or effort, not even a tiny bit. In the given context: "You got information and I want it. You could have said no and I might not have believed you. But you didn’t even say no. You’re not staying silent on me, my friend. Not six cents worth. Let’s go." It means the person didn't give any information or resistance, not even a little.

He probably used six, instead of two, as it alliterates and so is easier to read and sounds better. As dan says, it's just an arbitrary small number and there's nothing else significant about six.

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