(CNN) -- George Zimmerman's attorney says he's worried about the effect the "insensitive" tweets from his client's brother will have on the already controversial Trayvon Martin murder case.

Mark O'Mara says Robert Zimmerman -- whose tweets mentioned the suspect in the recent killing of a baby in Georgia and Martin -- does not represent his brother or the defense.

"Having said that, I'm not sure where (Robert's) heart was, but I've always said for the past year that we have to have a conversation about race, and the Zimmerman case has brought it to the forefront, particularly the way young black males are treated in the system," O'Mara said Thursday on CNN's "Starting Point." "These type of tweets ... were insensitive to that, and quite honestly are the opposite of what I hope the conversation would be to try and figure out what's wrong with the system and maybe a good way to fix it."

O'Mara said everything that happens in Zimmerman's case is already "hyper-focused upon."

"... And certainly when a family member of my client says something that comes across as totally insensitive -- if not much, much worse -- (it) has an effect, and now we have to deal with it."

George Zimmerman acknowledges he shot and killed Martin last year in Sanford, Florida, but said it was in self-defense.

His brother, Robert Zimmerman Jr., recently tweeted a photograph of Martin and one of 17-year-old De'Marquise Elkins, one of two teenagers charged with killing a baby in Georgia. Both teens are black.

In their photos, Elkins and Martin, 17, appear to be flipping off the camera.

"A picture speaks a thousand words. Any questions?" Robert Zimmerman's tweet reads.

Another tweet Robert Zimmerman posted: "Lib media shld ask if what these2 black teens did 2 a woman&baby is the reason ppl think blacks mightB risky."

Speaking on CNN's Piers Morgan Live on Wednesday night, he apologized for the messages, saying they weren't the "right thing to do."

"I realize those were controversial and offensive and I did publicly apologize for them," he said. "I'm a human being. I'm being upfront about what I did. I made a mistake ... Unfortunately (it) may not have helped George."

George Zimmerman has been charged with second-degree murder in Martin's death. Attorneys for Martin's family have accused Zimmerman of racially profiling the 17-year-old and shooting him "in cold blood."

Robert Zimmerman Jr. said he was trying to make a larger point in his tweets about the "media and their honesty in portraying the person who encountered my brother February 26, 2012.

"We've been led to believe that it's a junior-high-school-aged person because of the pictures," he said, referring to Martin.

"The analogy is these are two people who chose to represent themselves in this way. One was accused of killing a baby, and whatever's in his social media makes the rounds immediately ... However, the other person who almost killed my brother had he disarmed him -- my brother had every indication to believe he would have killed him -- his social media is off limits."

Martin family attorney Benjamin Crump said he agrees with O'Mara that someone should not be judged for what they tweet.

"But when it comes to Trayvon, they attempt to posthumously judge a dead teenager by his tweets and social media," Crump said on "Starting Point" Thursday. "And that is the problem here. You cannot know what is in a person's heart by reading a tweet."

The Zimmerman defense, Crump said, is seeking to introduce his client's social media activity as evidence in court.

"That's just not right," he argued.

"Starting Point" host Soledad O'Brien asked Crump about a witness identified as #9, which both she and Crump said is a cousin of George Zimmerman. The cousin called police a short time after Martin's shooting.

"Growing up they always made ...him and his family made statements like that they don't like black people if they don't act like white people. They like black people if they act white and other than that they talk a lot of bad things about black people," O'Brien read from the transcript of the call.

"Is this something that's going to be admissible in court?" she asked Crump.

The attorney replied that Robert Zimmerman's tweets "bolster" the testimony of that particular witness.