Beams would be too strong, particularly high intensity laser and tac lance. You would never be able to retreat and vent if the enemy was using beams properly. Big ships would not just be disincentivized, they would be really bad, probably useless. Speed would be the most important stat by far, kiting would be the optimal strategy... Also it becomes easier to track something at longer range, because the required angular tracking rate for a given target speed is lower. No thank you.
As I posted, "Targeting precision and optical weapon focus would need to be introduced to reduce damage at far ranges." Note that slug and missile weapons would still be deadly in comparison to beam. Beam weapons would lose focus causing less damage at a far range. Slug and missile weapons would do the same damage at distance. As long as they didn't miss.
Missiles shouldn't have a range limit but instead have an amount of fuel they burn through. Initial boost, stop engine and coast. Adjust direction, engine start to boost again, stop engine again and coast. Reach suitable distance to target, adjust direction and run-in boost. Lots of possible behaviors to differentiate the missile models.
If need be you could always increase the shield and armor of the larger ships in comparison to the small. It's not like I'd suggest to remove weapon range limits and make no other changes to compensate for that big change.
If you're going that far, ballistic damage should be based on relative velocity between the target and the munition. If the munition is moving in the same direction as the target it loses much of it's punch.