Ever consider having each side pick what weapons get damaged?   With the first weapon damage hit the owner of the ship getting damaged get to pick the weapons to damage, the second weapon hit allows the attacking player to pick the weapons to damage, then back to the owner for the third group of weapons, etc.

Otherwise ships can take a few weapon hits without hindering their attacking potential much.
Here's an example of a ship that can take two weapon hits and not have it's primary weapons systems affected at all.

Ship Exploiter
(230)
Shields: 3 3 2 2 1
Hull : 9-8-7-6-5-4-3-2-1
Engines: 4 4 3 2 1
Weapons: 17 14 11 7 4
Heavy Ion Accelerator *-12-18 1×3+/1/4 Bls; Cts
AB ☐ //1
Ion Accelerator 6-12-18 1×3+/1/2 Cts
ABCD ☐ ABC ☐ ABD ☐ //2
Aegis Array 1-2-3 2×3+/1/1 Dfn; Pnp
360° ☐☐ //1
Hyperdrive ☐ Tractor Beam ☐☐ ☐☐ ☐☐ ☐☐ ☐☐ //6

All 6 Tractor Beams will be damaged before any weapons will be.

What I'm proposing is that with this example, the first weapon hit will have the ship owner take 3 TB hits, then with the second weapon hit the attacker will choose 3 primary weapons.  To counter it, it's best to put about only 3 or 4 TBs on the ship, which seems more reasonable than having a bunch of "free" hits.

My first idea is to just alternate with every weapon instead of each group of the Weapons track.
Trying to make an SSD with a ship silhouette and systems spread throughout it just does not work very well with the current damage system.