If you hold a balloon by a string and the balloon moves towards your sweater and sticks there, what would you infer

That the balloon and the sweater have opposite charges. Remember, just like in the song, opposites attract.

The reason that the balloon will stick to the wall is because the negative charges in the balloon will make the electrons in the wall move to the other side of their atoms (like charges repel) and this leaves the surface of the wall positively charged