O'Mara told the judge that Martin's marijuana use and past fighting was central to the argument that Zimmerman used self-defense when he confronted Martin last year at a gated community in Sanford, Fla.
"We have a lot of evidence that marijuana use had something to do with the event," O'Mara said. "It could have affected his behavior."
An attorney for Martin's family, Benjamin Crump, said the teen's parents were pleased with the judge's rulings on information they consider immaterial to the February 2012 shooting.
"Trayvon Martin is not on trial," Crump said.
The judge ruled against a defense request that the pool of 500 jury candidates be sequestered during jury selection. She said jurors will be referred to by their jury numbers and prohibited their faces from being photographed. Nelson denied a prosecution request for a gag order that would prohibit attorneys from talking about the case.
O'Mara said he is concerned potential jurors could be affected by publicity the case is receiving.
The defense attorney had asked to push back the trial date because he said prosecutors had delayed turning over evidence as required. O'Mara is seeking sanctions against prosecutors, but a hearing on those sanctions was delayed until next week.
Before the judge decided to postpone the hearing on sanctions, a former prosecutor who used to work in the same office as the attorneys prosecuting Zimmerman testified he had told O'Mara about photos and text messages from Martin's cell phone that hadn't yet been turned over to the defense.
Former Assistant State Attorney Wesley White resigned last year from the State Attorney's Office that covers northeast Florida.