Combine tomato paste, water, crushed tomatoes, diced tomatoes, and basil in a large saucepan over medium heat; season with salt and black pepper. Bring to a boil, reduce heat to low, and simmer while preparing meatballs, 15 minutes.

Combine ground chicken, bread crumbs, Parmesan cheese, eggs, Italian seasoning, salt, and black pepper in a medium bowl; form into 1-inch balls.

Heat a large skillet over medium heat; coat with cooking spray. Add meatballs; brown on all sides. Transfer meatballs to simmering tomato sauce; cook until an instant-read thermometer inserted into meatball centers reads 165 degrees F (74 degrees C), about 30 minutes.

Bring a large pot of lightly salted water to a boil. Cook spaghetti in the boiling water, stirring occasionally, until tender yet firm to the bite, about 12 minutes. Drain. Serve meatballs and sauce over spaghetti.