Mr. Pucci is Dolores's high school guidance counselor who eventually transitions to her friend, although she's such a terrible teenager that we can't imagine why he wouldn't just celebrate her graduation and let her out of his life forever. But he doesn't—making him a good guidance counselor, we suppose—and instead he keeps subjecting himself to her bad attitude. He tries, and fails, to comfort her when Ma dies, but he still returns when Grandma dies. This goes a little better, and the two of them actually become friends.
Sadly, Mr. Pucci's lover, Gary, is dying of AIDS, and Mr. Pucci has it, too. Adding to Mr. Pucci's misfortune is that he's presented as super stereotypically gay, complete with "lispy speech" (8.2) and a roommate who wears cutoff shorts. That and Dolores calls him a "homo" (11.71) when she's a teenager.
But she mellows a bit as an adult, taking care of him as he slowly wastes away and even telling him that she loves him. We barely remember her telling anyone else that. In the end, he gives her a valuable life lesson in dealing with people: "Drink their milkshakes" (28.118). No, he's not trying to get Dolores to put on weight again, he's telling her she should let herself be loved.