Dr. Jekyll's wealth allows him access to the materials that he needs in order to create the potion that transforms him.  If you have ever conducted experiments, you'll know that usually it takes A LOT of time, materials, and money to go through all of the mistrials before you get a trial that works.  This is why universities need funding for all of their research.  Without money, research is greatly hindered.  His wealth also allowed him the freedom, time-wise, to conduct his research.  If he was off all day working hard to get a little bit of money that was barely enough to survive, he wouldn't have the time to experiment.  That excess of time also probably prompted his experimentation in the first place.  If you have a lot of time on your hands, because of wealth, you get bored and need stimulation.  Some people choose to take a cruise or skydive; Jekyll experimented and engaged his smarts.

His wealth not only allowed Mr. Hyde to come to pass, it also allowed him to stay around for so long without being caught.  Wealth allowed Mr. Hyde, when he did surface, to stay more anonymous.  Jekyll's wealth allowed him to clean up Hyde's messes, to help people to remain quiet and discreet about what was going on.  If you are poor, you can't really afford the resources to clean up messes.

I hope that those thoughts help some; good luck!