Is the cost primarily proportional to the size, or do inverters present a major fixed cost?
For the former it doesn't really matter how much you can cover, as it's simply an investment with a certain rate of return that has the amount you can invest limited by roof area.
I think all of the hardware will be very proportional to the size. In my case I had micro-inverters on each panel, so it was directly proportional, but this was actually more expensive than having a single large inverter (though more performant).
However, the marginal cost of things like engineering, installation and inspection will certainly go down with the size of the system. How much of that passes to the consumer I don't know, but some of it certainly does. You can imagine the cost of putting 1 solar panel on your roof is not going to be 10x less than putting 10 of them up there.
It is hard to get exact numbers from solar sites as they are very sales-oriented, but it seems like the hardware cost is estimated at anywhere from 20-50% of the total cost of the solar system. The rest of it is engineering, installation, inspection, customer acquisition, profit, etc.
For the former it doesn't really matter how much you can cover, as it's simply an investment with a certain rate of return that has the amount you can invest limited by roof area.