Proof: This is a simple matter of converting potential energy to kinetic energy where:

F(av)*d = 1/2 * (m(b) + m(s) + m(p)) * v^2

v = sqrt( (2*F(av)*d)/(m(b) + m(s) + m(p)) )

v = launch velocity of the projectile

F(av) = average force applied from the arm

d = draw distance as measured from pouch to epicenter of the strings

m(b) = mass of projectiles

m(s) = mass of strings

m(p) = mass of pouch

I hope it's evident to you, from the equation provided, that when you add more strings increasing the mass of the strings the launch speed of the projectile decreases. The most efficient slingshots are ones where string + pouch mass is minimized, and potential energy store potential is maximized.

Furthermore separating the string mass into separate strings makes the slingshot less efficient. Given the same average force, the draw distance of a slingshot designed with >2 strings will be smaller than the draw distance of a slingshot designed with exactly 2 strings (a simple proof of this involves simple trigonometry, while a more involved proof would also involve a bit of integration). Thus, given equal string masses and equal average force, the launch speed of a projectile from a 2 string slingshot will be faster than the launch speed of a projectile from a >2 string slingshot. The most efficient slingshots are ones where all string mass is concentrated within two strings. This is why most slingshots are designed using only two strings.