"That's the reason why I love acting, it is the opportunity to be different people and explore different facets of human life. Melbournites grew up with these guys on their front page every day, and everybody has a story, about them. You know 'I was in the pub when so and so met so and so', or 'My cousin's dog's previous owner used to go out with so and so'. Everybody has a story and a connection, so it's a great role to explore."
Grantley himself doesn't actually have one of those stories though - he grew up in Brisbane and wasn't particularly familiar with Williams when he first heard about the role.
"I went into the audition in a suit, and the casting agent was like 'Can you pull your shirt out?'" he laughs. "I'd done a quick Google, but I didn't really know he was a fat slob. Luckily I look a bit like him, and must've done a good audition, because I got the job, and then I really started to learn who he was."
Playing a man who died in 2010 at the age of 39, and is still fresh in people's memory was an interesting position for Grantley, weighing the responsibility to represent a real person with accuracy, with creating a compelling character.
"To me he'll always feel alive. He's sitting right in front of you," he says with a laugh. "That's what it's like for me. He's a shadow that will stick with me for a long time. I get called Carl 10 times a day every day, and that's just the way it is. I guess the way I think about it though, is that I played a character called Carl Williams. It's a true story, but they're not replicating the true story perfectly, so I try to think of him as a character that I get to inhabit and make my own, rather than trying to be the real Carl Williams."
It's not the first time he's played a real-life character. In 2009 he played New Zealand cameraman Gary Cunningham in the excellent film Balibo, which was about five journalists who were killed in East Timor during the Indonesian invasion of the 1970s.
"I actually met Gary's family ... he wasn't as well known as Carl Williams, but you feel a strong sense of respect and responsibility for playing a real person, whether they were good, almost heroic, like Gary, or not, like Carl. You want to represent them as well as you can. It definitely adds a different layer to your work."
Having been ensconced in Williams' underworld, it was nice to play a different kind of bloke - gay father Kane Albert in House Husbands.
The show has become very popular in Australia, and has been applauded for its portrayal of everyday dads and the inclusion of Kane as a gay character.
"The most important part there, is that the show really doesn't harp on about or focus on the fact that Kane is gay, it focuses on him as a Dad, who cares for his kids and is trying to bring them up as best he can. I think that's fantastic, because it's important that we portray gay characters on screen without making that a big deal.
"What Kane does in the bedroom should have nothing to do with the way he's seen in society or bringing up his kids. He's just another dad in this group of dads, who all have their struggles."
Grantley's enjoyed the response he's had from dads, whether they stay at home or not, and pleased to find how many people have found the show one they can relate to.
"I think people have seen it as highlighting this unspoken voice of the modern male. It's amazing how many house husbands there are these days."