Also, the show continuously develops Renton's phases of acceptance/understanding of Eureka.
From the beginning where he is infatuated with her, yet knows nothing about here, such as the naive kid he is.
Followed by her changes, he still accepts her and knows she is different, yet he still doesn't quite understand her and what it means.
Finally by the end of the show, the two have such mutual understanding that when he sees her yet again in a different appearance, he doesn't freak out nor make inappropriate comments as he would have before, all he needed to do was see her and just from the look in his face, you knew he understood how to approach her and how to act.
It's all about gradual development in a way that is believable over the course of time.
Kids take time to adjust and understand, it's a gradual change. Renton is pretty much *the* average kid, albeit sheltered. He has dreams, he has aspirations. He's a very realistic character, and he acts like one and makes decisions like one throughout the show. The show as a whole has a more "human" cast than 95% of other mecha anime.
Growing up doesn't happen over the course of a week after some girl magically pops out of a box.