Preheat your oven to 350°F (175°C) and grease a 9x5-inch loaf pan.
In a large mixing bowl, combine the mashed bananas, granulated sugar, brown sugar, and melted butter. Mix until well combined.
Add the eggs and vanilla extract to the banana mixture and stir until smooth.
In a separate bowl, whisk together the baking soda, salt, and flour. Gradually add the dry ingredients to the wet ingredients, mixing just until combined. Be careful not to overmix.
Gently fold in the blackberries, ensuring they are evenly distributed throughout the batter.
Pour the batter into the prepared loaf pan and smooth the top with a spatula.
Bake in the preheated oven for 55-65 minutes, or until a toothpick inserted into the center comes out clean.
Allow the bread to cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.