1. An image processing apparatus configured to generate a corrected image in which a deterioration caused by an aberration of an image capturing system is restrained, using a plurality of parallax images mutually having parallaxes generated by the image capturing system, the image processing apparatus comprising: at least one processor operatively coupled to a memory, serving as: (A) a weight generator configured to generate a plurality of weights as weighting data, each of which corresponds to one of the parallax images, based on one of pixel values and pixel value gradients of pixels at a same position in the plurality of parallax images; and (B) an image generator configured to generate the corrected image by summing up the pixel values at the same position in the plurality of parallax images using the plurality of weights, each of which corresponds to one of the parallax images.