Why broadside weight did not determine a ship's rate

How could a ship remain a third rate when its broadside exceeded that of some first and second rates?

Because the rate followed the number of gun positions, not the weight of shot the mounted guns could deliver.

The rating system counted how many guns a ship was pierced to carry. It did not rank ships by the total weight of shot in one broadside. British decisions to fit large numbers of 18-pounders could therefore produce a powerful battery without changing the formal rate in the way a modern reader might expect. The distinction separates an administrative classification from the fighting effect of the guns actually mounted.