This is a great question to consider. The text never openly states why it is that Dallas is so attached to Johnny, but if we look carefully at a few quotes we can understand why their relationship is so deep. To Dallas, who is a self-confessed down-and-out, somebody who has been in trouble with the police many times before, Johnny represents innocence that he wants to keep from becoming uncorrupted. Note what Dallas says to Ponyboy as they drive to hospital to see Johnny after the rumble:
I was crazy, you know that, kid? Crazy for wantin' Johnny to stay outa trouble, for not wantin' him to get hard. If he'd been like me he'd never have been in this mess...
We can infer that in Johnny, Dallas sees something of himself before he became corrupted and he is determined to try and keep Johnny from becoming "hard" like himself. The depth of his feelings for Johnny are shown in the way that he deliberately invites disaster after Johnny's death. In a very real way, Johnny's innocence was keeping Dally alive. Without Johnny, Dally felt he had no future.