Why are the proton, neutron, and electron, the masses that they are? 
Why are the proton and neutron so much larget than the electron?

The answer to your question is not known. Research is ongoing to
understand such issues.

Protons and neutrons are made up of three quarks each.  Electrons are
not made up of quarks, but are elementary particles themselves.  That
doesn't explain why they are the weight they are, but it does explain
why protons and neutrons are about the same mass, and electrons are
very different.

howdy.  From a fundamental point of view it is not even understood why
elementary particles have mass in the first place(let alone the
specific mass that they have!).  The mechanism many physicists look to
in order to give fields a mass term in quantum field theory is called
the Higgs boson.  The Higgs boson is a scalar field that somehow
"gives" mass to every other elementary particle through its
interaction with them.  The Higgs has a rather high threshold energy
for production, thus it has not been conclusively observed as of yet. 
That may change when the Large Hadron Collider comes online in ~2007. 
For an answer to your question supported by solid evidence, I'm afraid
that you are going to need 5*10^10 dollars rather than 5 :)