Ships get built at a fixed rate, dependent on their tonnage, racial tech, and governor modifiers. But it doesn't depend on the size of the shipyard. You can't build a corvette any faster just because it's in a battleship slip, basically. There's no benefit to building shipyards bigger than you need. Shipyards rated ABR is only for building the biggest possible ship.
However, shipyard mod rate DOES depend on the size of the shipyard. A 1,000 ton naval shipyard goes up to 2,000 tons a lot slower than a 30,000 ton naval shipyard goes to 31,000. I'm unsure if the mod rate is derived from the ABR or not, but probably. Mod rate tech just reduces the cost of modifications.
If you copy an existing shipyard but make it twice as big then check the estimated completion dates for the same ship.. you can see that it's identical.
numbers:
in my current game I have the "Grand Eagle" survey corvette which is 1000 tons with a cost of 214.8 BP and a build time of 0.64 years. This is a build rate of 335 BP/year, or about 0.33 build rate per shipyard ton. The 60000 ton "C-class" carrier has 8442 BP with a build time of 2.32 years: 3640 bp/year, with 0.06 build rate per shipyard ton. That's with a rated racial build rate of 560 bp/year.