Why does my paper airplane not look like a real airplane?
Most full size planes have wings, a tail, and a fuselage (body) that holds the pilot and passengers. Most paper airplanes have just a wing and fold of paper on the bottom that you hold when you throw the plane. The main reason why paper airplanes look different than real planes is to allow the paper airplane constructor to make a plane as easily and quickly as possible. The simplest airplane is the flying wing, and that's what most paper airplanes are.  Also, many features of a real airplane permit functions that a paper airplane simply doesn’t need.  For example, the flaps, which are the control surfaces on the edge of the wing, allow the plane to take off and land slower.  With a paper airplane, these functions are obviously not needed!

How does plane weight affect flight?
The simple answer is weight forward is good. In every object there is a center of gravity – a neutral point where all of the mass is balanced. If an airplane has a center of gravity ahead of the neutral point, then this plane is stable. If this center of gravity is behind the neutral point then it becomes unstable causing nose-dives and spins.

What really is stability?
Stability means that the plane, if disturbed, will return to its original state. A stable airplane tends to oscillate up and down a few times, but converge on a steady flight. Many typical paper airplane designs are stable, but just barely. A plane that is unstable will either pitch up into a stall, or nose-dive, but won’t settle out anywhere in-between.
As a plane becomes more and more stable, it wants to fly faster and faster. To counter this tendency, up elevator must be used to produce a good trim airspeed. This is why many of the classic paper airplane designs are nearly neutrally stable. Few people realize good pitch stability requires a heavy nose and some up elevator. The classic designs rely on the small inherent "up elevator" effect (positive zero lift pitching moment) resulting from the swept wing, and possibly the airfoil shape. Thus many classic paper airplanes can be flown with no elevator adjustment. Sometimes they fly well, many times they don't, and they always have poor stability.

What is the importance of winglets?
The Fuselage acts like the vertical stabilizer of real airplanes. Sometimes bending the wingtips up on paper airplanes also helps to add directional stability. The combination of the fuselage and wingtips on paper airplanes allows them to have positive directional stability. This stability is provided in real airplanes by a vertical tail.

Does material matter?
Paper airplanes usually have short "stubby" wings, called "low aspect ratio" wings. The distance from wing tip to wing tip is called wing span, and the distance from the front to the back of the wing is called the chord. The ratio of wing span to average chord is called "aspect ratio", and is an important characteristic of wings. Paper is a lousy building material. There is a reason why real airplanes are not made of paper. Although high aspect ratio wings reduce drag, they also require better building materials. The low strength of paper does not allow the use of high aspect ratio wings. With a thicker material or paper, it is easier to make planes with high aspect ratio wings.

For more information on airplanes, real and paper, check out:
Paper Airplane Aerodynamics: http://www.geocities.com/CapeCanaveral/1817/paero.html
How to Make a Paper Airplane: http://home.inreach.com/jdcard/engl3007/airplane.htm
Exotic Paper Gliders: http://www.people.cornell.edu/pages/rwa2/airplanes/index.html
Joseph Palmer's Paper Airplane: http://www.josephpalmer.com/planes/PL1/PL1.shtml