The wiki doesn't have the exact numbers, but I believe it's dependant on the primary weapon group and it's more than just 2x. I'm playing on a server that requires turrets to have a max range of 2 sectors for lag reasons, and I had to rework my Cannon-Beam-Punch turrets and Missile-Beam turrets from 100% beam support to keep them from shooting too far.
I haven't done this, but it would be a good experiment, fire up single player and make a 10 Cannon and 10 Missile systems on a test ship, then try adding a beam support system of 1 through 10 blocks and checking the range at the different values. You can click on the weapon system line in the ship's system view to expand it and then click on the blue details button. That will give you a breakdown of every group of weapons tied that weapon computer, and from there you can get all sorts of detailed info including range.
That way you could check the range boost of the weapon system at 10% increments to get a feel for the numbers.
I've been pretty happy with the performance of the light turrets ball turrets I came up with for a light cruiser I've been working on for way too long now. Initially I had them in light railcannon configuration, 130 Cannon - 130 Beam - 130 Punch, and they basically put a one block hole 20 to 40 blocks into a target depending on what they hit. I ended up swapping out the beam support for Damage Pulse support when I made my ship server compliant, and I haven't tested the penetration in a target yet, they put holes straight through smaller ships.
