I too thought that the energy charges having weight was completely absurd... but then it occured to me that might only apply to a chemical battery. A Fallout energy charge might be a unit of plasma and gas and stuff. Especially when we are talking Microfusion Cells.
A microfusion cell is supposed to be a self-contained fusion reactor, this is explicately explained by the item description in Fallout 1 and 2. This means it has a certain amount of fuel (hydrogen, or helium III) and that stuff undergoes fusion. The whole point of fusion is that it is very energy efficient, a large amount of the mass is converted into energy. Which powers your weapon. Also, the stuff that has fused together will probably be hot plasma... and perhaps that in itself is directly used by your energy weapon. In Fallout 3 there's a terminal in the outcast base that says a plasma rifle directly taps into and fires the plasma from the microfusion reaction. (On the other hand, this terminal gets the stats for the ammo capacity of laser and plasma weapons completely wrong, so it must have been written early in development and its canonicity is debatable.)
In Star Trek, the starship Enterprise has an antimatter reactor and its reaction produces large amounts of hot plasma. Rather than then converting this into electricity, this plasma is in fact pumped all around the ship. All the power conduits are full of plasma, even the lights and the control consoles and the monitor screens have circuits where tiny currents of plasma travel through them, rather than metal wires conducting electrons.
When you think about it, this seems rather technically unfeasible, and also quite dangerous... and it is actually the in-universe explanation for why it is that when the ship is damaged the control consoles explode in showers of sparks. A simple computer console can lose magnetic containment and explode, heh. Which also leads to the amusing fan explanation of "Why doesn't the Enterprise have seat belts? Well, would you really want to be strapped to one of those exploding consoles?!" But for the big energy users like the warp engines, and the phasers, and the shields, this direct usage of plasma makes some sense.
Anyway, it occurs to me that perhaps Fallout energy weapons work the same way. Hot plasma could be fed directly into a laser rifle, and since plasma is charged like electricity it can directly power the laser, or perhaps it gets converted into traditional electricity inside the laser rifle. While in the case of a plasma rifle, it just fires the plasma out of the front of the gun.
As you use up a microfusion cell, there is less fuel in it, and the plasma is used by the gun, so the cell gets lighter.
In the case of Small Energy Cells and Electron Charge Packs... hmmm. The Fallout universe has never bothered to explain what a Small Energy Cell actually is. It could be a very advanced chemical battery. Or perhaps nuclear fission. But then there's the fact that New Vegas lets you use different type of energy cells to charge each other up!
Perhaps a Small Energy Cell is a container of plasma. It doesn't even necessarily have to be HOT plasma - everyone has seen those lightning balls where you press your hand to glass and electricity jumps to your fingers. So SEC contains plasma, and a Microfusion Cell is a tiny reactor that actually converts some fuel into plasma. What's an Electron Charge pack? Dunno, but I guess it stores electrons. I suppose that if you removed all the protons and neutrons from a substance you'd just have a sort of negatively charged electron plasma.
So, yeah, all the energy cells are actually full of "pure, concentrated energy", a plasma of particles that is fed directly into the weapon. So the cell can actually get lighter when drained.
Oh, except for the fact that hydrogen, helium, and plasma are all significantly lighter than air, so the idea of an energy cell having signifcant weight and then that weight dwindling to nothing as the energy is drained doesn't really work cause of that.
But, it does still make a certain amount of logical sense, the energy cells are being depleted in the same way that a magazine of bullets is depleted.
Yup, you can fire the Tesla Beaton with a meagre 1 cell instead of needing 45.
You know what, that's actually quite useful, because some of my suggested upgrades were for Energy Recyclers in the style of the Laser RCW recycler. But I feared that it could cause problems in weapons that used 2 or 3 energy per shot, as you could end up with just one ammo left in a weapon that requires two energy per shot.
In Fallout 3 a weapon would NOT fire if it didn't have quite enough ammo, but the game wasn't smart enough to then do the normal automatic reload you'd get when you actually depleted a magazine, so instead you'd be left going CLICK CLICK CLICK. This was a nightmare in VATS, cause the character would continuously go CLICKCLICKCLICKCLICK for about TEN SECONDS until the game returned you to real-time play and you could then hit R to manually reload.
So yeah, it seems that because Obsidian made lots of the energy weapons require multiple ammo per shot, they anticipated that sort of situation and changed the game's ammo-use logic. It's the better of two evils.