I don't think I explained it very well, though. Look at it this way. Think about trying to throw a rock off the roof of the house at the ground to hit a tin can, then think about throwing the same rock from the yard at a tin can up on the roof. Your throwing arm knows the physics even if your brain doesn't. It takes a lot more oomph to throw upwards to counteract gravity. And the upward velocity will be slower. But you air rifle can only throw at one speed.
The earthward acceleration due to gravity is 32 feet per second squared. The downward velocity increases exponentially with time, so the arc of the bullet in flight is parabolic. The faster muzzle velocity of a lighter pellet means the pellet gets to the target in less time, in the flatter part of the trajectory curve, up to a point, but not necessarily with greater energy. Conversely, heavier pellets, longer time to target, and a faster drop, but their forward momentum means a slower drop in velocity. The same inertia that makes the heavier pellet harder for the compressed air to it accelerate down the barrel, resulting in lower muzzle velocity acts to make the pellet harder to decelerate due to air resistance once it leaves the barrel.
This means that heavier (more massive) pellets carry more forward, down-range energy per unit of time than lighter pellets, independent of the drop due to gravity. In a vacuum the parabolic arc of "Gravity's Rainbow" would be the same for .177 and .22. In air, with forward resistance, the .177 is going to decelerate at a faster rate and though in a horizontal trajectory it has a flatter initial trajectory, its velocity is going to drop more rapidly and the effect of gravity over time will be more pronounced. So, at the end of the trajectory curve, it will be falling at a relatively higher higher velocity than a heavier pellet. The ballistic coefficient (BC) tells you about how a pellet will decelerate in air relative to a known reference projectile, but BC's for air gun pellets are petty meaningless, it turns out.
But once you start shooting upward, not only air resistance, but also gravity work to uniformly decelerate a pellet. Lower velocity = longer time of flight to the target = more downward velocity or drop of the pellet before it reaches the target. And when you compensate by aiming higher, the actual distance traveled by the pellet to a target, for example 50 yards down range, is no longer 50 yards, because the pellet isn't traveling in a straight line, it's traveling in a longer arc, and will take more time to reach the target, and will drop more due to gravity in that time, and will need to be compensated for by aiming higher . . . So, mathematically, you can't hit there from here (LOL).
Bottom line - forget all the calculations and BC's -- just understand in general what forces are working on the pellet once it leaves the barrel, and then go to the range or to the hills and figure out what your gun does with the pellets you are shooting. Mr. Barnes begins to look even smarter.
BTW, regarding air temperature, the Cardew brothers (my new techno-geek heroes) took a test rifle and wrapped the compression tube in heating and refrigerating jackets, let the air in the compression tube come to a uniform temperature, before cocking the springer, and then looked at muzzle velocity. Guess what? Little or no difference over a wide range of temperatures. Only when they heated the compression tube to the point that it began to vaporize the oil in the compression tube (at temps where the tube was too hot to touch) was there substantial difference in measured muzzle velocity, and that was due to excessive dieseling or detonation. So forget ambient air temp affecting initial muzzle velocity -- it doesn't, no matter what the calculations say.
So show me an air gunner with a calculator or a laptop with a ballistics program trying to figure out where the pellet is going to land, and I'll show you a man in trouble. Time to go to the range and practice some more.
