The centripetal acceleration due to the earth's rotation does reduce a person's weight. The effect is greatest at the equator because the centripetal acceleration depends on your distance from the center of rotation. The effect is very small. At the equator expect your weight to decrease by only 0.3%. A 150 lb person would only lose a half pound.
A fun question I like to ask on exams is, "How long would earth's day be if the earth were spinning fast enough to cancel your weight at the equator?" My answer in next post.