Here is the diagram featured in the game's manual, which I assume you never read.

Don't worry though, it's wrong. The top and the bottom are switched and some of the highlighting is misleading.
Here is my corrected diagram with added numbers for reference.

1. Aft section of the conning tower
   
2. Tip of starboard wing*
   
3. Tip of port wing*
   
4. Top of starboard nacelle
   
5. Top of port nacelle
   
6. Rear hatch
   
7. Bottom of nose
   
8. Bottom amidships
   
9. Bottom of port nacelle
   
10. Bottom of starboard nacelle

* The red sections on the original diagrams indicated where cosmetic damage would show once that weak-point was destroyed but NOT where specifically to shoot. Fortunately, this is only a problem for #2 and #3. I've found the optimal target point for these two weak-points to be from the front as shown here.
Only shooting the front tips of the wings will damage the weak-points' hitboxes.

Top down views of the frigate.
Notice, only the forward portions of the wings are circled.

Bottom up views of the frigate.

NB: The nacelles have separate weak-points on top and bottom (4, 5, 9, 10). The wings only have one each (2, 3).


Top

Bottom

Here is the diagram featured in the game's manual.

Again, some of the highlighting is misleading.
Here is another corrected diagram with added numbers for reference.

1. Top hatch amidships
   
2. Fore section of conning tower
   
3. Port bow "gills" on bottom
   
4. Starboard bow "gills" on bottom
   
5. Ribbed section amidships
   
6. Debossed segment on port side pontoon
   
7. Aft section of port side pontoon
   
8. Bottom hatch amidships, between two reactor-looking structures
   
9. Debossed segment on starboard side pontoon
   
10. Aft section of starboard side pontoon

Top down views of the cruiser.
Not many weak-points up here but lots of plasma turret defenses. You'll want to spend most of your time battering these guys from underneath.

Bottom up views of the cruiser.


Top

Bottom

Notice that the cosmetic damage indications for weak-points 3 and 4 (the gills), once destroyed, match what the original manual highlights indicate are the weak-points but the true hitboxes are much shorter.

Here is the diagram featured in the game's manual.

It is.... COMPLETELY CORRECT! Surprise!
Nevertheless, here is mine with added numbers for reference.

1. Base of fighter catapult
   
2. Base of fighter catapult
   
3. Base of fighter catapult
   
4. Base of fighter catapult
   
5. Turret tower
   
6. Turret tower
   
7. Base of fighter catapult
   
8. Turret tower
   
9. Turret tower
   
10. Base of fighter catapult
    
11. Base of fighter catapult

Yeah, this one is pretty straight-forward. Just remember weak-points #5, 6, 8, and 9 are the tower structures the turrets sit on, not the turrets themselves.

Top down views of the carrier.


Bottom up views of the carrier.


Unlike the cruiser, the top of the carrier has a dangerous amount of plasma turret defenses to match the large number of weak-points located there.