Symbolism, Imagery, Allegory
You Raise Me Up
Balloons are just... happy. They don't appear in too many of the stories, but when they do, balloons are a reliable source of joy. In the first episode of the tales, right after Pooh falls into the thorny gorse-bush (itself a constant symbol in the books) he immediately thinks of something to lift him back up to achieve his goal of getting the honey. That something: a balloon.
That's right. From the very beginning, the balloon is an object that helps our characters achieve happiness. So later in the book, in the chapter in which Eeyore has a birthday, Piglet naturally chooses to give him a balloon to make him happy. After all, "'Nobody can be uncheered with a balloon'" (Winnie-the-Pooh.6.59). We and e.e. cummings know this is true.
It's the Thought That Counts
It's not just the balloon itself that is important to Milne, but the idea of a balloon. Eeyore shows us this by getting happy (Eeyore! Happy!) about his balloon even after it gets popped. The balloon was his favorite color. It was his favorite size. For Eeyore, the balloon represents the idea of a gift, of a celebration, of joy. And since we see balloons associated with the same concepts throughout the tales, we can guess that Milne feels the same way. He is using his characters to show us this. If gorse-bushes are the symbol that brings the characters down, balloons are the one that lifts them back up.