She lingers there, because being affectionate with Harry has always been completely easy for her, even when she's interrogating the depth of her feelings for him. Also, because the man just continuously looks like he is in need of a hug.

"Harry, of course it meant something," she murmurs softly, squeezing his shoulder. "All you've been through, everything that's been demanded of you - I'm going to harp on about how you deserve a break forever, but I don't want you to think that it's been for nothing. You have no idea - the students, Harry. They're so different from what we were like when we were little, it fills me with such hope to see it - Slytherins and Gryffindors huddling together to study. Bloody hell, even the Quidditch games are full of genuine sportsmanship, and none of that peacocking everyone did when we were in school ourselves. You did that - you made that hope possible."