Before you start shaking your head and shouting "No!" at your computer screen and preparing an angry email about how stupid we are, hear us out. Our host Jason Fenske from Engineering Explained is referring to the addition of weight when traction is limited, such as in snowy or icy conditions. In this video, Jason explains it perfectly and does all the math so you can stop composing your email now and just enjoy the video.
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When you have limited traction because of the prevailing conditions, a rear-drive vehicle with a light rear end won't accelerate well or and may not go anywhere at all. In this case, the problem can be fixed by adding some weight. Plop a few sand bags in the back of the truck bed so it sits over the rear axle, and the added weight will actually improve your ability to accelerate.
You've just increased the amount of traction you'll see because you're helping push those rear tires into the ground. So, yes, in this instance adding weight improves acceleration. It also increases fuel consumption and reduces your ability to slow the vehicle down with braking.
It's only useful in this specific situation. Once you're no longer traction limited, you will not accelerate better with that added weight, and you'll still suffer those penalties. With that in mind, sure to remove the sandbags come spring.