I may be completely out to lunch with these points. I frequently am. But this is how I think about casting:
Line & fly are cast by the Kinetic Energy you generate in the line via rod tip speed.
KE = .5 mass of the line x velocity ^2.
Heavier lines are easier to cast than lighter lines.
Because you can more easily cast them before you develop the casting skill to put more velocity into the line, via rod tip speed.
Lighter lines are more difficult to cast than heavier lines.
Because they require more velocity to generate the same amount of KE that is more easily attained by casting a heavier line with lower line velocity. And it takes time to develop the skill to cast a line with higher line speed.
It is easier to load the rod more with a heavier line than with a lighter line.
It is easier to generate a higher rod tip speed with a longer rod than shorter rod. Up to a certain sweet spot of rod length. Longer pendulums weigh more and move slower than shorter ones.
Longer lines are more difficult to cast than shorter lines.
Longer lines will have more mass than a shorter line of the same size, but they slow down rod tip speed, require more casting skill to generate the required velocity. Because KE in the line will decrease by the reduction in v^2, which has a larger effect on KE in the line than the increase in weight of the line.
Heavier or bushier flies are easier to cast with a heavier line.
But can be cast with a lighter line after you develop the skill to cast the line with a higher velocity. But maybe it is easier to use a heavier line when casting bushy flies or heavier flies. I must confess I seldom use bead head flies.
If you are trying too hard to cast the line and not having success.
Your timing is poor. You’re failing to fully synchronize the motion of your casting stroke with the rebound of the flex of the rod. And the energy from the rebound is not being added at the right moment to increase line kinetic energy.
It’s easier to put more energy into your forward cast if you properly load the rod during the back cast.
A 4号 line has 2x the mass of a 2号 line if they are of equal length.
To double the KE in the line, 200%, you can either double the weight of the line ( change from 2号 line to a 4号 line) or develop the casting skill to increase line velocity by 41.4%.
As you can see it will be easier to get more energy in your cast by changing to a heavier line. A heavier mono-filament line or a furled line. All you need to know how to do is how to tie on a different line. Or conversely if you change from using a furled line to a lighter mono-filament line, you will need to learn to increase your line speed to put the same amount of energy into the line.
And the only way to increase line speed is practice, practice, practice. Or rather practice perfect. Repetition of the wrong casting stroke with wrong timing will only ingrain poor form. But I believe if your mind knows what needs to be done - your subconscious will lead you to improving your casting distance and accuracy, no matter what weight of fly you are casting.
[oh, Speed and Velocity are both distance ÷ time. But Velocity has a specific direction. Otherwise the same thing]
Maybe I know the difference between shinola and the stuff laying on the ground. Or maybe not. 
But thinking about casting this way works for me. I’m sure other people think about casting in a different way that is equally valid or maybe a better way to think about it.
