Like all other plants, they put a lot of effort into developing the baby pumpkins. To the plant it doesn't matter how big the fruit grows as long as it produces seeds to enable the pumpkin family to continue for future generations. So the plant churns out a lot of flowers and a lot of baby pumpkins. A lot of small, baby pumpkins. Humans, particularly Americans, think bigger is better.
To get big fruit you need to threaten the plant. When the vines have many babies growing along them, they'll send relatively equal amount of nutrients to each so that they can all grow and develop. When some of those offspring suddenly disappear, the plant boosts the energy to the remaining fruit so that they'll grow quickly and overcome whatever catastrophe caused the loss.
You need to be that catastrophe. With just a few weeks before the first frost, time becomes an adversary when it comes to growing big pumpkins. By plucking off flowers and pruning very small fruit, you divert extra energy to the remaining parts of the plant. When only one or two pumpkins remain on the vine, all of the energy from those large, elephant-ear leaves flows to them. The boost is enough to cause a perceptible size increase.
To get big pumpkins, first look at the flowers. After you have the young pumpkins on the vine, remove the flowers that can develop into competition. To make it easy, remove them all. To save effort, look closely at them. Male flowers will be on long, thin stalks. Female flowers will grow on shorter stalks with a very small bulb at their base; that is the baby pumpkin in the making. You really only need to remove the female flowers to prevent additional pumpkins.
You can also remove fruit of any size that has already developed in an effort to boost the size of the remaining ones. Use pruning shears or a sharp knife to separate them from the plant. The vines can be prickly so it's a good idea to wear gloves. How many you remove is up to you.
A typical vine will produce up to five pumpkins, potentially more. Competitive pumpkin growers will select the single, fastest-growing pumpkin on a plant and remove all others. That's one way they grow monstrous pumpkins. If you're growing for Halloween carving, you may want to keep one or two of the pumpkins that are perfectly shaped and remove ones that don't match up. If you're going for size, keep the biggest and remove all of the small, developing ones. If you want quantity, be happy with the three or four that are doing best and sacrifice the rest; accept that they all won't reach their full size potential.
My best vine has two pumpkins that are already growing past 10 inches in diameter. They look great and I'm very happy with them. Another on that vine is about eight inches and there's one more about the size of an orange. Though I'd like all four, the smallest just doesn't have enough time to develop in the two or three weeks remaining before our potential first frost. To benefit the other three, it has to go.
My wife planted her own vines in a separate bed a few weeks after I did. The late start is reflected in the size of her pumpkins. They are just now approaching the softball stage. To have any hope of sizable fruit on her plants we have been systematically removing all of the flowers and will soon remove some of the small pumpkins once we determine the best candidates. We may be left with a single pumpkin on each vine to hope for a harvest.
You probably aren't growing a champion pumpkin over 1,810 pounds (the current record). You just want some that will delight your kids or grandkids, or make a good pie. I don't like to unnecessarily harm or prune any plant, but when it comes to pumpkins, selective pruning will provide the best results. In many respects, for pumpkins size does matter.