"Some closure" for family of "American Sniper" Chris Kyle

There is "some closure" for the families of "American Sniper" Chris Kyle and his friend, Chad Littlefield, after Eddie Ray Routh was sentenced to life in prison for the 2013 murder of their loved ones.

"I think it's still early," Chris' younger brother Jeff Kyle said Thursday on "CBS This Morning." "It hasn't quite set in just yet ... but it definitely helps. And I think it will put an end to a chapter in our lives."

Routh killed Kyle and Littlefield at a Texas shooting range on Feb. 2, 2013, after Routh's mother asked Kyle to help her son. Routh told authorities that he was a former Marine suffering from post-traumatic stress disorder.

The families waited two years to hear the verdict, and according to Jeff, they had a feeling the jury would find Routh guilty.

"But you never know," he said. "It could go either way, and you can't spend the entire time watching the trial and trying to read them. They're not going to show their hand."

They felt good up until the moment the jury stepped out to deliberate, he said.

"We had no idea at that point where it was going to go, and that's when the thoughts start racing and you just pray it's going to go right."

Their initial sense turned out to be right, and the jury convicted Routh of capital murder. Jeff said Chris' wife, Taya, was "very relieved."

"We haven't talked a lot since then. She sent me a text yesterday saying, 'Amen, we've got a verdict.'"

The murder trial captured the country's attention, especially after the release of "American Sniper," the Oscar-nominated film based on Chris' military career. While Jeff didn't find anything to be untrue in the reports about the trial and Chris' life, he pointed to one thing his brother would have had distaste for:

"The hype, he hated the hype."

The trial was even dubbed the "American Sniper" trial.

"I know Chris would be upset about that," Jeff said. "To us, it's not the 'American Sniper' trial; it's a trial about Chris Kyle and Chad Littlefield. And I think too many people forget about Chad and about who he was. He wasn't a veteran, but he had the heart and soul of a warrior and was doing everything he could to help out as many veterans as possible."

Jeff Kyle, who is also a military veteran, described Chris as "larger than life" and said he missed Chris' "smartass little self" the most. Chris was not only a great father, brother and son, but also an "outstanding man."

"He cared about everybody. He gave everybody a chance, and gave his life doing what he loved."

While Jeff called his brother "an average, everyday guy," Chris was known to be one of the most lethal snipers in American military history. After four tours in Iraq, Chris returned home and devoted himself to helping other veterans reintegrate to civilian life. He created the Guardians for Heroes Foundation to help military personnel combat PTSD.

"He wanted everyone to have the chance to come home, and once they came home, he didn't want it to stop there. So he was helping on and off the field," Jeff said.

For Jeff, having to see his brother's killer repeatedly during the trial was one of the hardest things he's ever done.

"Just seeing him in there, just no remorse -- that was very difficult. There were a lot of times when I wanted to get up, but, you know, he's not worth my time."

Along with the prosecutors, the Kyle family decided to seek life in prison for Routh, not the death penalty.

"Of course we wanted death penalty, but I guess we still wouldn't have a verdict. We wouldn't have closure right now even if we would have gone with the death penalty," Jeff said. "It would still be going on."

During the trial, Routh's lawyers pursued an insanity defense, and even mounted their evidence with the fact that Chris texted "This dude is straight up nuts" to Littlefield the day they were killed.

Jeff, however, never bought it.

"I use that term all the time. Chris used that term all the time. If he would have thought that he was nuts, if he even had a little bit of an idea that he was nuts, it wouldn't have turned out the way that it did."