I can’t get beam weapons to work on fighters. Is there some inherent limitation that prevents their use on those size hulls?
Absolutely. Look closely in the textfile for whatever module it is you’re experimenting upon. There is an attribute code for weaponry which puts them into one of three classes: cruiser, frigate, and fighter. Unless you alter the value of a given module’s attribute to allow function on a hull other than what Cliff intended, then function it shall not. For all I know there may be additional integrity checks which the game app makes on the back end in order to prevent what you’re thinking of. Please do report back here with results of your experiments, okay?
As far as I know changing the “Size” entry from FRIGATE to FIGHTER will make it work but you also need to set the “crew_required” entry to 0.
Also, don’t forget to change the turret image size to zero, or you’ll have a capital ship turret taking up 1/3 of your fighter’s image.
Nothing wrong with a big gun on a little ship. 
That’s quotable. Jackie Fisher probably said something like that during the Great War when he came up with the concept behind the British Royal Navy’s HMS Furious: a shallow-draft light cruiser for shore bombardment…principal armament being two 18" guns! A rather extreme expression of your idea. 
Sometimes its all about completely silly designs. Like this tank:
en.wikipedia.org/wiki/Landkreuze … 00_Monster
see cliff? that tank is COOL
i told you vehicles built around a single huge gun are cool
especially if the gun has enough power to turn several city blocks into a glassy crater in one pop
Just to clarify, I took the entry for the cruiser laser, re-worked the stats so they would be appropriate for a fighter including crew requirements and size line and turret size, and the game crashes when I try to save a design with that module attached.
I think the beam weapon template just flat out doesn’t work on fighters.
I’ve been using beams for some time now without trouble:
Did you type FIGHTER in the size entry all in capitals? If not that might cause problems.
If that’s not the case, post up your module file and we’ll see what’s causing the issue.