There's a part of him that wants to kiss it off of him.
There's another part that makes him want to bite it off, wishing his teeth were strong enough not only to gnash through metal, but through all that it signifies. It's a jealous, petty part of him, a desperate part of him that wants and needs and wishes that he were far more capable of reaching out than he ever has been before.
There's a part of him that's begging from the inside out, tentatively reaching but still not finding that to be enough.
He wishes it had been that hand that grabbed his own to stop him from running after Lunatic. Barnaby's noticed the ring before, but he wishes he knew what it felt like, metal grazing against his flesh. He sort of wishes he knew what it felt like to have that ring on his finger, or at least, something akin to it.
He's jealous, and he's inadequate, and it hurts - because he's not enough, he never will be enough, and he can hear it and feel it in the reverent way that Kotetsu talks about her and everything that she was.
But honestly – it's a little better this way, lest they somehow become something, and either of them lose another person yet again.