As of when I posted this, the only lasers being deployed as weapons are HUGE, take a lot of power to operate, and are only capable of damaging small objects.
Is that necessarily so, though?
A 20kW laser only consumes about 100kW (well, only... but still). Military lasers are megawatt rather than kilowatt, but they do not really need to be. Laser engravers are typically considerably less than half a kilowatt, CNC lasers with 1 to 2 KW cut straight through metal plates (of a reasonable thickness), and 20kW lasers are being used to drill through massive rock, but even that feat isn't necessary.
The idea of shooting your lasers pheeeeeouwwww pheeeeeeeouwww in as Star Trek like manner and then the target spectacularly exploding is fun for television, but that's it.
Other than a drone or a missle (or any physical object with significant mass) a laser beam can be targetted and retargetted in very little time. Actually it almost only depends on how fast you (or your targetting computer) can react.
The target needs not explode because you make a pheeeeeouwwww sound and because that's cool. It's sufficient if the laser tracks the drone/missle for 1-2 seconds, heating the missle head to 250-300°C and causing all electronic circuits to fail. That's something 5kW can easily achieve, no need to atomize it (it'll do that by itself when it hits the ground).
Even so, putting a megawatt laser into an airplane is not impossible at all. Pratt & Whitney demonstrated in 2012 how it is feasible to turn a civil aircraft engine (such as you'd find on a Boeing 747-400) into a 120 MW power generator.