As soon as Yuki gets mentioned, I become a watering pot
I guess Uenoyama realises how big this is for MAfuyu. It's like this last message from Yuki that Ue wants Mafuyu to have. Especially considering how Mafuyu always wished to talk "one last time". It's Ue's way to make Mafuyu happy and truly be able to move on. Also, he acknowledges Yuki's feelings being different from his own- and very important to Mafuyu.