Girls that Grow?

[CacoVenom]

Sousei No Aquarion is sad
Boku Wa Tomodachi Ga Sukunai, get over a break up or friendship
Black Rock Shooter, friendship

[EkaCoralian]

Maybe wait an episode or two, but I think Ritsuko from Sakamichi no Apollon would work pretty well.

[Chained(E)Studio]

Thanks for the suggestions, please feel free to post more if you think of any as this project will be going on for a bit.

[SatoshiSakura]

Maybe Natsuiro Kiseki?

[Rider4Z]

at first i thought you meant "get bigger" in which case i would have suggested Hare+Guu

[Magicflier]

When I read your description, the first thing that came to my mind was Mahou Sensei Negima!, though only manga-wise sadly.. the anime barely follows the manga.

Saki fits your description pretty well, so does:
Binbou Shimai Monogatari
Da Capo II (though the focus is more to the sad parts though, before she grows..)
Eiyuu Densetsu: Sora no Kiseki (not sure about the anime's genre though)

Hope these might fit your description?

[Magicflier]

I've forgot to mention Kimi ga Nozomu Eien, this anime is possible