Stan taking the “death” of Wax Stan way too seriously is one of my favorite jokes in the show. In all likelihood, it is just a joke about how egotistical Stanford Pines is.
But, if you want to hate yourself, here’s another way to look at this. Stan has someone (well, something) that looks exactly like him. He watches tv with Wax Stan. He cracks jokes at Wax Stan. He’s got pictures of himself with Wax Stan. Until Wax Stan is murdered, that is. What does Stan do? He buys a coffin. He hosts a memorial service. Perhaps, because this time around, Stan has a body to bury.
Goofy, egotistical old man? Yeah, probably. It’s a silly show after all.
Grieving twin staring into the face of the man who was taken from him thirty years ago?
Well, why not?