Doyle's one of the good guys, but he tries to keep his head down. He's not going to rock the boat or make any waves, even after his son, Joey, gets murdered. When the cops ask him about what caused Joey's death, all he says is:
POP: No idea.
And he tells a neighbor, Mrs. Collins, to be quiet when she starts talking to the cops about how Joey had the courage to stand up to Johnny's gang.
This isn't because he's a wimp. It's more because he wants to make sure Edie, his daughter, is safe. But Edie's got plans of her own, struggling to discover the truth about Joey's death. Pop urges her to go back to the private college she's attending and stay away from Terry, but she can't.
Even though he's worked so hard for Edie and Joey that one of his arms is shorter than the other, it's a losing battle for old man Doyle. Edie's going to do what she wants to do. Fortunately, it doesn't work out badly. Turns out Pop's method of keeping his head down wasn't necessarily the right way to go, since Edie, Father Barry, and Terry finally bring the mob down.
So, maybe Pop Doyle will start doing some pull-ups and Tae Bo and assert himself more in the future.