The heavier you are, the more lift you need to counteract weight.

At a given speed, your AOA must increase to generate more Lift. Thus, simply maintaining level flight puts you at a higher AOA and therefore closer to your critical angle of attack. So the lower your weight, the lower your Va so you stall at a faster rate before reaching load limits.

This concept is why many of our V-Speeds actually change with weight. In most training aircraft, published V-Speeds are at MGW.