Considerations are peak and average thrust (force) and distance. Traction(potential force) is related to modulus of the rubber. Also, there is the matter of internal friction and inertia. In other words, the harder the band is to lock in, the higher the peak thrust and also this; commercial latex has varying properties determined by the manufacturer. In today's world, these manufacturers are responsive to requests from spearfishing vendors and have designed special formulations. Biller coated amber rubber has a rep for being soft. So, one may find that a sample of black or amber rubber from somebody like Neptonics may have significantly more "snap". In fact, several vendors, including on EBay and elsewhere, also sell the same, so called, high modulus rubber. Now, to the physics.
You might be able to estimate the kinetic energy by measuring the peak force in pounds and the distance travelled. That would be the distance from full tension to relaxation. This is defined as "work", W = f X d........work equals force X distance . Weight or "mass" of the arrow is important as is the average force of the rubber band which I guess could be defined as peak strength in pounds divided by two. Whatever amount of work is done requires an equal kinetic energy to perform the work. KE = 1/2 mv^2......also F = ma (Newton's second law). A force with an average value of 50 pounds pushing two pounds over three feet is addressed by F = ma with the result; a = 25 fps^2........we know that v = at and also, S = 1/2 at^2 where S is distance of band travel..........solving the second equation for t we get 1/2 sec. Inserting the time and accelleration into v = at then the velocity is 12.5 ft/sec. KE = 1/2 mv^2 = 156 ft-lbs.
We can see from this, v = at and KE = 1/2mv^2 that the energy of the arrow is proportional to the square of the velocity. So, velocity is very important and this is directly related to distance and force. Also, it makes sense to increase the force by installing thicker rubber and that a small difference in stretch is not as important as average force. For example, it is apparent that increasing force by 30% would be a good trade off for increasing velocity and energy even when losing 10% of pull length (W = F X D).
As a practical matter, due to internal resistance and inertia of extremely thick bands and, on the other hand, low traction of the small bands (being a function of total mass and modulus of rubber), that a mid size band would be more efficient if it can be cocked without undue increase of length and consequent shortening of travel. Remember, the volume of rubber and total mass of rubber increases much faster than the diameter of the band, simple geometry of a cylinder, so small changes in diameter have a big influence on several things. My conclusion is that two, 5/8 bands will produce the best solution of energy delivered. However, it may be a good idea to learn chest loading as this is a principal means to improve pull strength.
PS
It would be beneficial for a spearfisherman to learn to fabricate bands from bulk rubber so as to allow some experimentation without excessive cost.
Pesky
