Barry doesn't see it to begin with, he's just trying to keep up with everything that's going on around him. Working with Jane was a learning experience, and it was sometimes a struggle for him to keep up, but once he'd learnt the ropes, he'd started to notice the little things.
It's the little touches he notices. The two of them were always touching each other, seemingly not even noticing it themselves. A little hand brush here, a gentle hand on the small of the back there. He'd even seen them brush the hair out of the face of the other with a gentle caress.
But they clearly had no idea, and it wasn't just one-sided either, they both touched each other so often Barry had no idea how someone hadn't mentioned it to them. He didn't dare, Jane was his partner and he wasn't afraid to admit he's slightly afraid of her, and Maura was always so understanding about his issues with the bodies he didn't want to upset her either.
As he watched them now, he saw Jane put her hand on the small of Maura's back as she directed her friend towards the lift, both of them talking animatedly. He smiled to himself, they had to work it out at some point, and he hoped he was there to see it.