I agree with all that, which is why we have things like Great Wyrms. But an animal is only an animal, it isn't magical, so it should act normally.
First, why assume that a square-cube law even exists in a fantasy universe? Stuff on a material plane can be made out of fire, water, earth and air instead of atoms. Even for "natural" creatures, you can throw conventional physics and chemistry out the window.
Second, there's a spell on the animal. If spells can violate laws such as conversation of energy, I don't see the square-cube law as much of a problem.
Finally, on point, Animal Growth
does note that "This spell does not affect Colossal creatures." That seems like a pretty clear indicatation that the designers intended the spell to work on anything smaller (regardless of hit dice).
I agree it could be powerful and that it is slightly unusual. Most other "buffing" spells provide a flat bonus instead of a bonus that increases with the strength of the creature. But the creature should also become the center of attention for a targeted dispel magic. Maybe the best thing is to run it as written and find out.