The second factor to consider assuming they have reached their maturity as per the cultivar, is how big the variety you planted is supposed to be. Are you sure you didn't plant a personal or mini style watermelon ?
Watermelon Transplant damage
If you started your watermelons from transplants as opposed to direct seeding, there's a possibility you damaged the roots when doing so.
Damaged roots can't always take up sufficient nutrients to support the hefty growth rate of watermelons. Deep cultivation too close to the plant can also cause root damage.
Pollination of Watermelons
Pollination is needed to produce quality watermelons. If weather was poor at pollination time, chances are your vines did not get as much traffic from bees and butterflies as they should have. Poorly pollinated plants will produce fewer watermelons, smaller melons and substandard ones. Inter planting a diversity of plants that attract bees in the vicinity helps to attract pollinators and reduce the risk of inadequate pollination.
The primary reason for small melons is temperature. Watermelons thrive in the dog days of summer, they are heat lovers. A minimum of 60 degrees, but preferably more than a tad higher is needed. Lower temperatures leads to a slower plant growth and ultimately stunted melons that are usually substandard in other mannerisms as well. Best day time temperatures for Watermelon is 80 to 90 degrees, night time no lower than 60 degrees F.
Who put the Water in the Watermelon ? You did - I hope. If you didn't that's another reason why your watermelons may be stunted and substandard. Watermelons love the heat, this is true, but they also crave moisture. Watering is critical to producing quality watermelons. The key time to water is from the time the fruit begins to form until it is half-grown. As harvest time approaches you need to cutback on the watering so the fruits can concentrate their sugars. Excessive watering too close to harvesting of watermelon will reduce the sugar content and cause the fruit to have hollow centers.
Check the soil moisture daily or more in hot arid and dry weather and water as necessary. Always allow the top inch and a half of soil to dry between re watering . Watering early in the morning is best so leaves will be dry by sunset, this will help to curtail fungal diseases. Some organic mulch wouldn't hurt either. just around the base.
Plant Damage and Disease
Aphids are a common culprit for smaller melons. Usually in an aphid infestation the fruit is also distorted and misshapen. [See: Aphid Control] Aphids also spread a disease known as Watermelon mosaic virus which also leads to stunted growth.
Nematodes. They are microscopic worms which that dwell in the soil and feed on the host plants roots preventing them from taking up the nutrients they need to grow. Beneficial nematodes added to the soil will help prevent another occurrence.