Kingsley allowed both Weasley's to come along with him as he was sure Molly truly did need the support. And Arthur as well, grappling with the knowledge that his wife had been that close to a mass murderer.
Also, when they got to Tonks' house it turned out that their son was there too. So he's extra glad he agreed. He just wishes he'd been warned about that in advance so that he could warn the Weasley's; he knows his expression didn't change when he saw the children so the couple probably think he didn't warn them on purpose.
He then gets his first look at Sirius Black. It's underwhelming. For the world that grew out of the war You-Know-Who's name was too taboo and terrifying for people to discuss, his most trusted follower – Sirius Black – became the bogeyman people were allowed to scare children with.
Not in the auror offices, of course, not with Alastor Moody breathing down people's necks and watching their every move, and only getting more paranoid when he hears the name of his old student mentioned.
Kingsley never worked with Black during the war but had seen him around in between moments; the same way he had with the Longbottoms, or Johnny Dawlish's older brother – Black had been a carelessly dangerous man then. Kingsley hadn't been very surprised to learn he was hiding something.
There's nothing careless about him now. The danger is still there, but it's become feral from being outcast – and Kingsley can see how someone might miss it if they want to. Someone like Tonks, who made sure that of all the things they were known for, blood had never been one of them. Someone like Mrs Tonks, who had made her stance quite clear in her interviews. Someone like Harry Potter; a young boy with more family issues than both of them put together.
Black watches Kingsley carefully. He'd expected to see the madness of a cultist in his eyes but it isn't there. Nor is any sort of smirking sadism or carefully controlled cunning. Kingsley has met a lot of villains during his career.
Sirius Black reminds him of none of them.