Arthur Weasley is the ultimate paterfamilias, which makes sense given that his wife is the book's mother figure. Combined, the Weasley parents are the book's major parental figures. In fact, they're really the only parents we see at length and in depth in Book 3.
Mr. Weasley is an ideal dad in a lot of ways. He's wise, has a great sense of humor, and is one of the few adults wiling to treat Harry like a smart, mature kid on his way to being a grown-up.
We trust Arthur's judgment and Harry clearly does too, since he remembers his words in a tense moment:
But as he stood there, flooded with excitement, something Harry had once heard Mr. Weasley say came floating out of his memory.
Never trust anything that can think for itself, if you can't see where it keeps its brain.
The map was one of those dangerous magical objects Mr. Weasley had been warning against [...] (10.3.50-52)
Like a good dad, Arthur's words are influential and stay with you. He definitely serves as a father figure to Harry. As Molly has a connection to Lily, Arthur has a clear link to James as one of the book's fathers. Like James, Arthur is brave, is willing to stand up for his family, and is levelheaded in a crisis. But it's notable that, while Arthur is a father figure to Harry, he isn't the only one. Harry also finds father figures in Dumbledore and in Remus Lupin. So, while Arthur and Harry have a definite bond, it's not quite of the same nature as the bond that Harry shares with Mrs. Weasley, who has basically adopted him into her brood. Arthur treats Harry with a respect that isn't quite what you'd expect to see with a father and a thirteen-year-old son.