Well hear out would be used if you expect the person to not finish listening to what you're saying out of principle. If you're saying listen to me carefully it would imply that you do expect them to listen to what you have to say, but they might not be paying close attention. If you're just saying listen to me, then it would be a case that you don't expect them to listen to you, but it's not really that they have anything against it, just that they weren't going to do it, it's a very neutral statement.
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