If you produce 500 pizzas per day, and 1,000 people want pizzas. You don't get rid of the backlog by doubling the size of the pizza. Either you produce 1,000 pizzas per day, or you increase the price so that 500 people buy something else.
Not quite. In Adam's analogy, 1 pizza = 1 tx. By doubling the blocksize limit, you're not making bigger pizzas (tx sizes don't change).
What's happening is loosely this:
Right now, a pizza delivery guy leaves the pizza shop roughly every 9 minutes. Today, his car can fit 500 delivery orders; after the block size increase, 1000.
P.S. re. "spam transactions":
The pizza shop get all sorts of orders called in -- some people just order a Coke, because too lazy to hit the bodega themselves. Smallblockers will have you think that the best way to deal with this is by keeping the Isetta delivery car, so no more than 500 orders will need to be delivered every 9 minutes.
This is stupid: just like the pizza shop, the miners can (and do) reject any order they don't feel like dealing with. They may choose to deliver Cokes to build up clientele, or charge $20 to deliver a Coke to your door.
Keeping a small delivery car simply means your pizza business can't grow