Given that GZ didn't know Trayvon, the past conduct wouldn't give GZ any additional reason to be suspicious of him. But it would demonstrate Trayvon's predisposition to want to settle disagreements with his fists, and DD's testimony shows he wasn't happy about being watched. The lends credence to GZ's assertion that Trayvon started the fist fight.
TM’s past conduct is a good sign that GZ was telling the truth about what he observed on that evening. The media from the beginning tried to paint him as a bigoted white man who just assumed that a young black male was up to no good. I’m afraid the jurors may give greater weight to the media version more than to what they heard in the courtroom.