I'm no melon expert either but I agree, Aphids could very well be the culprit on your
Watermelon (Citrullus lanatus 'Sugar Baby')
Aphids cause stunted growth and curled, twisted leaves. You can use an Insecticidal Soap (found at most garden centers) for aphid control.
There is also a virus called Squash Leaf Curl Virus that affects watermelons too but usually with that disease the leaves have a lot of yellowing along with the curling.
http://www.plantwise.org/Knowl...