http://www.bowlingfans.com/jeff/ballreactionbasics.htmlTop/Bottom WeightAs mentioned previously, bowling balls come with extra weight placed under the center of gravity punch on the ball to balance out the weight taken out by drilling holes. This weight is called top weight because it is located in the top of the bowling ball. Bowling balls generally are manufactured with anywhere from two to four ounces of top weight although it is possible to find balls that fall outside that range. Lightweight balls are made with less top weight generally for two reasons. Light balls generally are drilled for children so the holes are smaller, meaning there is less weight removed that needs to be balanced out. Also, since the ball has less total weight, an ounce or two of top weight will have more effect on the ball's dynamics and throw them "out of whack."
Top weight has a similar effect as finger weight: the ball will go longer down the lane and snap a bit more on the backend. Likewise, bottom weight is like thumb weight in that it makes the ball roll earlier and arc more.
Unlike other static weights, ABC/WIBC regulations allow up to 3 ounces of either top or bottom weight. This is measured on the dodo scale by comparing the drilled side of the ball (top) to the non-drilled (bottom) side of the ball.
Top and bottom weight are not necessarily caused by shifting the CG away from the center of your grip. They are more a result of how much extra weight the manufacturer placed in one side of the ball and how much weight is removed from that side during drilling. However, you can alter top weight and bottom weight by shifting the CG. Because top/bottom weight are measured by comparing the grip side of the ball (the top) to the non-grip side (the bottom), if you shift the CG away from the center of the grip, you are moving it around the circumference of the ball towards the bottom. You would be removing top weight (and/or adding bottom weight depending on how you look at it) by shifting the CG. Therefore, the most top weight you can have in any particular ball after drilling (and before drilling any extra holes) would be if the CG is directly in the center of the grip.
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To the OP, what is the track of the bowler that said that? I once had a driller tell me that because of my low track, that top weight would be like additional side weight for me.