Consider using minicapacitors that ships charge up and allows for a few shots while at speed.
...and not so much at providing power to weapons
Or, simply, much like the jump drive, the weapons pull (or require) more power than the plant can provide over a short time.
Consider. crudely, that a laser takes twice as much power as the plant can give (for assorted hand wavy values of "power").
The way to solve this is through a capacitor, which, like a xenon flash of old, can provide the discharge energy necessary for a single shot. But it takes "two turns" power up the capacitor.
Now, you can look at this like a ship wide weapon capacitor grid. It starts with, say, 20 points and the plant can charge 4 points per turn. And the ship has dual, triple laser turrets. Each laser shot takes 1 point. Each "double laser" shot take 2 points. You can see how the ship has the ability to make several shots in a row, but will soon find itself behind the ball.
The other option is to make the capacitors tied to each weapon.
What distinguishes a military vessel is more space to the capacitors (for longer sustained combat), or larger plants to drive the weapons.
"Doctrine" suggests using the capacitors for weapons as Capacitor...uh...capacity is smaller than Power Plant capacity. Simply, the power plant necessary to constantly drive 2 triple turrets would be larger, and much more expensive, than the capacitors to back them up. So, it makes more sense considering the rarity of combat, the lower maintenance of capacitors, the smaller tonnage requirement, etc. to use smaller plants and more capacitors than large plants to drive them all.
Obviously the ratios need fiddling with.
You can also add a mechanic of capacitor leakage. You can't, shouldn't, and don't leave the capacitors constantly charged. It would be a routine step when about to take flight to charge the capacitors first. But, you certainly wouldnt leave them charged up in dock, etc. etc. A catastrophic capacitor failure can be quite violent, so leaving them charged while docked is risky and frowned upon.
This opens up RP opportunities when players need to get out of Dodge quickly.