"You know how there is famously no place less played in than a hospital playground? ... I mean, how could you dump her? She's dying." (11.172-175) Augustus lost his previous girlfriend because of the infamous asshole cancer that turns the sweetest of people into firebreathing demons. What he gained out of that is experience and so he knows that he doesn't have a predicament as bad as Carolines. This helps him appreciate life more.
"YOU CANT KILL MAX MAYHEM!" and with a final flurry of button combinations he dove onto the grenade..." (4.59) Sure, they didnt really lose too much, its just a video game but since he dove onto the grenade Hazel gained the comfort of knowing hes willing to do whatever it takes to protect her, even if she is a grenade.