While I agree that jealousy is atleast an element of Chuck's character, I never found myself agreeing with the consensus that him not telling Jimmy that his mother said his name to be an indication of his shittiness. Not that it was a good thing to do, but...well, consider it from his perspective.
First, he is sitting in the hospital devastated that his mother is dying, while Jimmy seems to be considerably less affected. Different people show their grief in different ways, but Jimmy, to Chuck's perception, seemed to be barely grieving at all, and not unreasonably so. Ch
Second, why do people think his mother saying Jimmy is proof that she loved him more? The woman is dying and clearly in no way cognizant. She might be saying Jimmy because she just happens to see Jimmy in whatever dying dream she has. She could just be reliving some kind of memory or something. Sure, Chuck is sad that he can't get through to his mother, that she can't hear his voice through her delusion. And that's heartbreaking. That it's Jimmy she's thinking off also stokes the fires as well, but honestly, if that happened to me, I would be anguishing that my mother couldn't hear me as well, whoever she was calling out to.
What I always got from that scene is Chuck's silent rage that the world doesn't work the way it's supposed to. Chuck is beside himself with grief, while Jimmy barely seems to care, yet it's Jimmy that she thinks of. Chuck is the one who stayed with her to the very end, while Jimmy went on a food run, yet it's Jimmy she that she calls out to.
So while there was a resentment to be noted on Chuck's part at the hospital scene, I didn't feel it was one of jealousy. That vice feels too small and petty. It's resentment at the injustice of the world, where Chuck did what he was supposed, but Jimmy got his mother's last thoughts. And if that happened to me, to my mother, while the other close family member barely seemed to care, I'd be furious too. And that's not being petty, vindictive asshole, that's just being human.
Edit: and just to be clear, this doesn't mean Jimmy is doing anything wrong or that Chuck is being fair here. He's not. It's just weird to people saw all that and went "Aha! Even his own mother didn't love him and he's jealous of Jimmy. Yet another reason why he's a shit!" instead of basic empathy that anybody in that state wouldn't be at their best regardless of who they are.