It became associated with black culture because black people tended to have larger backyard gatherings, which means feeding a lot of people. They are also historically marginalized, and had lower incomes as a result. So not only were they feeding more people when they had parties; They were doing it for cheaper. Watermelon is a cheap and easy way to feed a dozen people, and fried chicken is cheaper than other forms of protein like steaks. Yes, both are delicious, but the stereotype happened because it was both cheap and could be served in large quantities for larger backyard parties.