Yes, anything will technically weigh less at the Earth's equator compared to other parts of the world, say the North or South pole. Any object weighs lighter in the equator, because it is farther from the earth's center of gravity as compared when it is weighed in the Northern or Southern Poles. You see, the earth is not a perfect sphere and it is "flattened" at the poles because of the rotation of the earth. Thus, the earth's gravitational pull on an object is greater in the either poles than at the equator.
Furthermore, the acceleration due to the rotation of the earth also affects the weight of an object in the equator. The centrifugal force tend to "throw it off" away from the planet. There is no extreme rotation at the poles so weights of objects are not affected.
However, it doesn't mean that you will weigh significantly less in the equator so don't pack your bags yet and relocate there. The weight difference of objects in the equator and in other parts of the globe is extremely small (less than 0.5%) that you won't even notice it with an ordinary weighing scale. Simply put, if you are fat in New Zealand, you will still be fat in Ecuador.