If you're a powerlifter, this phrase might've been engraved on your blood-stained weightlifting belt by your great grandma, Mabel. Basically, the statement refers to a greater ability to lift a load due to an increase in body weight. Initially, this statement might appear to make some sense (which is why it's hung around so long), but once you understand the details, it's just plain dumb. A physicist would slap you in the face with a pocket protector if you said this in his classroom.
Here's a sample scenario for you to ponder. Let's take a 200-pound weightlifter with a maximum squat of 400 pounds. We'll call him Sammy No-Squat, since he's as pathetic at squatting big iron as Ray Mentzer was at explaining biochemistry. Sammy decides to hire a powerlifting coach to improve his miniscule squat numbers. The coach takes one look at Sammy and says, "Boy, you need to put on some weight if you wanna squat big!"
So Sammy spends the next six months eating everything under the sun. At the end of six months his body weight has escalated to 240 pounds. Sammy retests his squat, only to find out it didn't improve one bit! In fact, it was a little harder to lift the same amount of weight. How can that be given the staying power of the powerlifting phrase, "It takes weight to lift weight"? Let me explain.
When you perform a squat with just your body weight (no external load), you're moving approximately 75% of total body weight. Therefore, if 200-pound Sammy performs a body-weight squat, his muscles are actually lifting about 150 pounds of weight. To take this a step further, if the heavier 240 pound Sammy decides to perform a body weight squat, his muscles have to lift 180 pounds of weight. It's easy to see in this example that he has to lift 30 pounds more body weight due to his feeding frenzy. Now let's carry over these numbers to the weight room.
When the lighter Sammy squats with 400 pounds of iron on his back, his muscles have to lift a total of 550 pounds (400 pound load plus 150 pound body weight). Given the same load, the heavier Sammy has to lift 580 pounds (400 pound load plus 180 pound body weight). So now, Sammy's 400 pound squat takes more effort to lift at his new, heavier body weight. He has to lift 30 pounds more weight! Combine this with the fact that he didn't change his squat routine (i.e. he didn't get any stronger) and you'll understand why his squat didn't improve with a heavier body weight. His muscles have to produce more force to lift the same load!
Now, I must state that an increase in body weight will help you push more weight, but we're talking about lifting more weight. Also, more body weight may aid your efforts when attempting to lower a load due to the laws of physics, but the last time I checked, no one was handing out trophies to the person who could lower the most weight.
Also, there's the theory that increasing the girth of your waist (i.e. base) will aid your efforts at the bottom of the squat when reversing the movement. In most cases, I've found this to be unnecessary. By utilizing the correct coaching tips, I can get my clients to expand their waist enough at the bottom to achieve the same effect without making them add eight inches of blubber to their waistlines by overeating.
Now, you might be thinking, "I know tons of lifters who improved their powerlifting numbers by gaining weight, so that statement must be true." Sure, many have, but their strength was from an increased level of muscle, not body weight. If a lifter was on any decent weight-training program and consuming a hyper-caloric eating plan, approximately 60% of added body weight would be from muscle. Therefore, if Sammy gained 40 pounds of body weight, then 24 pounds of it should've been muscle! Obviously, 24 more pounds of muscle due to sarcomere (muscle fiber) hypertrophy will make you stronger! Therefore, the phrase should be restated as, "It takes more muscle weight due to sarcomere hypertrophy to lift more weight."
So don't think you have to lose your granite mid-section just to squat or deadlift more weight. Add muscle, not plain old body weight, and don't forget that extra body fat will probably hinder your efforts to squat and deadlift more weight.