Why does Hyde grow stronger when Jekyll stops using the drug?

In Robert Louis Stephenson's The Strange Case of Dr. Jekyll and Mr. Hyde, Hyde not only grows stronger over time: he becomes larger, stands more upright, and finally does not need the drug at all to appear. In fact, Jekyll needed a serum to prevent Hyde from appearing. Over time, Jekyll would need stronger and stronger doses of serum. Finally, they no longer worked. At that point, Jekyll takes his own life to prevent becoming Hyde permanently.
Stephenson was from a devout Presbyterian background. The message of the book is that evil, once you set it free within yourself and indulge it, will inevitably take over, rule your life, and damn your soul. There is also the interpretation, however, that to believe oneself to be without sin is itself a sin: pride. This is what Jekyll does by concealing his inner sinfulness even before taking the potion to transform himself into Hyde.