They cant try him again, unless there is new evidence.
Nope. They can't try him even if he screamed out "I really really really did it!" They can't try him if he showed them a video of him killing her.
I'm not trying to convict him in a court of law. So I don't need tons of evidence. I just need a mind.
That's the excuse people like you always use: I am not a judge/we're not in court. Doesn't matter where you are, give him the same fairness you'd expect for yourself. Make the prosecution prove that he truly did it. If not, all you can do is say "Uhhhh...I
think he did it."
but they didn't have enough proof to give him death
That's not how the U.S. criminal system works. You only prove whether the defendant is guilty of something. As for what happens to him, the prosecution has no say, and the prosecution's evidence is usually not used in determining if someone should get death. Usually, the nature of the crime is used to determine that. You can't say: well, they brought enough evidence for life in jail, but not death.