Story highlights George Zimmerman's attorney said he is concerned about how tweets could affect case

Robert Zimmerman tweeted side-by-side images of Trayvon Martin and De'Marquise Elkins

Elkins is accused of killing a baby in his stroller in Georgia; Martin was shot by George Zimmerman

"I'm a human being ... I made a mistake," says Robert Zimmerman Jr.

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."

Photos: Photos: Trayvon Martin evidence Photos: Photos: Trayvon Martin evidence Trayvon Martin evidence – A photo posted online Monday, December 3, shows George Zimmerman with blood on his nose and lips. His attorneys say it was taken the night unarmed teen Trayvon Martin was killed in Sanford, Florida. Zimmerman, 28, faces second-degree murder charges in the death of Martin in Sanford, Florida, on February 26, 2012. Other evidence photos were released earlier this year: Hide Caption 1 of 10 Photos: Photos: Trayvon Martin evidence Trayvon Martin evidence – Zimmerman says he shot Martin in self-defense. Martin's attorneys say he was shot and killed "in cold blood." Hide Caption 2 of 10 Photos: Photos: Trayvon Martin evidence Trayvon Martin evidence – Zimmerman said that before he shot the teenager, he was "assaulted (by Martin) and his head was struck on the pavement," according to a police report. Hide Caption 3 of 10 Photos: Photos: Trayvon Martin evidence Trayvon Martin evidence – According to a fire department report, Zimmerman had "abrasions to his forehead," "bleeding/tenderness to his nose" and a "small laceration to the back of his head" when he was treated at the scene. Hide Caption 4 of 10 Photos: Photos: Trayvon Martin evidence Trayvon Martin evidence – In a photo released by the Sanford Police Department, Zimmerman's hands appear to be unmarked. Hide Caption 5 of 10 Photos: Photos: Trayvon Martin evidence Trayvon Martin evidence – Prosecutors allege Zimmerman unjustly killed Martin, an unarmed teenager, after profiling him. Zimmerman has pleaded not guilty and claims self-defense. Hide Caption 6 of 10 Photos: Photos: Trayvon Martin evidence Trayvon Martin evidence – Zimmerman's gun is displayed. The shooting raised questions about gun laws, as well as the merit of the "stand your ground" law in Florida and similar laws in other states. Hide Caption 7 of 10 Photos: Photos: Trayvon Martin evidence Trayvon Martin evidence – Crime scene photos released by the Sanford Police Department show Trayvon Martin's cell phone at the scene of the shooting. Hide Caption 8 of 10 Photos: Photos: Trayvon Martin evidence Trayvon Martin evidence – Evidence marker 2 shows a plastic sack found at the crime scene. Hide Caption 9 of 10 Photos: Photos: Trayvon Martin evidence Trayvon Martin evidence – A can of Arizona iced tea was found on the ground at the Martin crime scene. Hide Caption 10 of 10

Photos: Stigma for town in Trayvon Martin killing Photos: Stigma for town in Trayvon Martin killing Stigma for town in Trayvon Martin killing – Memorials to Trayvon Martin grow daily outside The Retreat at Twin Lakes, the gated Sanford, Florida, community where neighborhood watchman George Zimmerman shot and killed the unarmed teen February 26. The death has sparked protests across the country and brought unwanted attention to Sanford, a town north of Orlando. Hide Caption 1 of 11 Photos: Stigma for town in Trayvon Martin killing Stigma for town in Trayvon Martin killing – Sanford's main roads are dotted with mini strip malls in between patches of what remains of central Florida's agricultural history. Views about the Martin case depend on which streets you stand on in Sanford. Hide Caption 2 of 11 Photos: Stigma for town in Trayvon Martin killing Stigma for town in Trayvon Martin killing – "I don't see Sanford as being a prejudiced town by any means," said Michelle Simoneaux, left, manager of downtown's Colonial Room Restaurant and Fountain. "This could happen anywhere, but it doesn't happen every day. " Hide Caption 3 of 11 Photos: Stigma for town in Trayvon Martin killing Stigma for town in Trayvon Martin killing – A neighborhood watch sign marks the gated community where Martin died. Zimmerman has said he killed the teen in self-defense, police said. Hide Caption 4 of 11 Photos: Stigma for town in Trayvon Martin killing Stigma for town in Trayvon Martin killing – Members of the Goldsboro community play a game under an oak tree. Goldsboro was one of Florida's earliest towns incorporated by African-Americans before Sanford absorbed it and took over in 1911. Residents speak of frequent police patrols in the area and other cases similar to Martin's. Hide Caption 5 of 11 Photos: Stigma for town in Trayvon Martin killing Stigma for town in Trayvon Martin killing – A protest sign painted on the window of a car at a housing project calls for Zimmerman's arrest. For some, the Martin case has become a rallying cry, a chance to air what they believe are years of grievances. Hide Caption 6 of 11 Photos: Stigma for town in Trayvon Martin killing Stigma for town in Trayvon Martin killing – The Martin killing has been the subject of intense coverage in local newspapers as well as the national media. Hide Caption 7 of 11 Photos: Stigma for town in Trayvon Martin killing Stigma for town in Trayvon Martin killing – Longtime resident Myranette Boynton, 58, says she thinks the attention to Sanford will make a difference. "This occasion has happened too many times, and enough is enough," Boynton says from the banks of Lake Monroe. "Trayvon is not the only one, but Trayvon should be the last one." Hide Caption 8 of 11 Photos: Stigma for town in Trayvon Martin killing Stigma for town in Trayvon Martin killing – A handwritten card lies among the memorial gifts outside the neighborhood where the high schooler died. Hide Caption 9 of 11 Photos: Stigma for town in Trayvon Martin killing Stigma for town in Trayvon Martin killing – A woman strolls through the downtown area. Many residents say they wonder whether Sanford will forever be known as the place where an unarmed black teen was killed while heading home from the store. Hide Caption 10 of 11 Photos: Stigma for town in Trayvon Martin killing Stigma for town in Trayvon Martin killing – Signs about the shooting have been posted throughout the Florida city, and the message is clear: People want answers. Hide Caption 11 of 11

"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.