This is a very popular question I receive and thought I would post it up. The answer is yes and no.
Moment of Inertia (MOI) - The moment of inertia, otherwise known as the angular mass or rotational inertia, of a rigid body determines the torque needed for a desired angular acceleration about a rotational axis. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rotation. It is an extensive (additive) property: the moment of inertia of a composite system is the sum of the moments of inertia of its component subsystems
What this basically says is with mass, more power is needed to rotate on a given axis. If the rotating mass is closer to the body, less force is needed to rotate and when mass is further away from the body, more force is needed to rotate. So in softball terms, balanced = easier to swing, end loaded = harder to swing and heavier bats take more force to move vs. lighter bats. Lets use an example
30oz vs. 26oz bat (balanced or end loaded -- same model different weight):
Using the same person, lets say the swing speed using a 26oz bat is 85mph. When he picks up the 30oz, his swing speed diminishes to 75mph. As rotational power (torque) has lessened, the drop off in acceleration translates in less distance as it is greater than the pick up in mass. So the answer to this scenario of "more distance" is NO.
Now lets take another person using the same example. Swing speed of a 26oz bat is 85mph and when going to a 30oz is 83mph. Because the drop off in acceleration is less than the pick up of mass, this would translate into greater distance. So the answer is YES
So what am I getting at?
What this means is total mass (weight) does have an effect on distance, however, if you simply cannot generate enough bat speed to overcome the mass, then you are not doing yourself any favors and actually going backwards. You should ALWAYS choose a comfortable weight and balancing # 1, and 2, swing a weight you can consistently swing the fastest.
When altering a bat, we can simulate more mass in a lighter bat by simply shifting the weight around inside of it. Not to get to technical, but typically speaking, there is more "play" in an end loaded bat vs. balanced as far as shifting weight around. This is because on an end loaded bat, most the weight is in the cap which is accessible. On balanced bats, the weight distribution is in the hands and a lot of times, not accessible to be shifted around. So basically, a factory end loaded bat gives you more options as far as weight "re-distribution".
When manufactures develop bat technology, they have to account for the type of material in relation to how it breaks down and flexes at impact. This is how bats get the BPF rating and limitations are set. All that goes out the window when altering a bat as weight can be shifted around to maximize wall flex as well as thinning them out by shaving. As mentioned, end loaded bats are harder to swing because the weight is on the end, however, if you can leverage that weight, once the bat begins to rotate, it pulls itself through the zone with more force due to the increase mass. The barrel will actually flex around the ball and not deflect.
Balanced bats tend to slightly deflect off a ball because the mass is stored in the hands and not through the contact point. This doesn't mean balanced bats do not hit, it simply means there is more deflection in relation to end loaded bats. This is why an end loaded bat will always out distance a balanced bat holding common variables the same....basically more trampoline effect.
So in summary:
1) Pick a comfortable weight/balancing combination you can put a "good" swing on the ball. If it is a 26, then 26. If its balanced, then balanced. Don't trick yourself into thinking making some adjustments will yield greater results because chances are it will set you backwards. If you are new to the game and still figuring this out, then I can see that, but if you are an established player and have tried out some equipment, chances are you stick to what you like for a reason.
2) Once you have settled on a weight and balancing, pick a shave spec that meets your goals and expectation
Using this method, 1+2 will yield MAXIMUM RESULTS for your swing type and capabilities.