Let me explain you it differently - a skilled light fighter is supposed to outmaneuver a VHF due to its better agility and therefore probably kill it (snub pilots correct?).
Therefore a skilled light battleship will outmaneuver a heavier battleship due to better agility and other factors.
Liberty does not need heavier battleships, infact the Liberty Dreadnought is one of the best battleships out there simply because its far more agile than most other battleships, in the right hands it can kill any other battleship, your lack of experience with capitals just blinds you and you can't see the logic here.
Now as far as the carrier's concerned, Tabris' quite right, you shall avoid engaging with other battleships in a carrier, but however the LAC can possibly outmaneuver a turtle and if you know what you're doing, you can actually kill them.