Sounds like you need more downward tracking force. After you zero out the tonearm (making it float) you then move the plastic ring on the counter weight (NOT THE WHOLE COUNTER WEIGHT, just the plastic ring!!!!) to "0." Then move the counter weight (NOT JUST THE PLASTIC RING, both the weight and ring!!!) to the recommended tracking force of 1.75 grams.

Yes, the manual completely sucks! When purchasing a new turntable a good dealer should offer to set it up for a nominal cost, if not for free. Watching how it's done and asking a few questions is never a bad idea. One of these makes it easier.

http://www.musicdirect.com/product/74340

It also sounds like you had the anti-skating engaged while you balanced the arm to set tracking force. Anti-skating should be set to zero while you do tracking force; once that is set, do anti-skate.
Bottom line: if you have a lousy manual and don't have previous experience in setting it up, take it back to the dealer ASAP for them to set up!

Check this youtube video out. It looks like it is a comprehensive and easy to follow guide to setting up the Debut III.

Good luck.

http://youtube.com/watch?v=1MIK9WcSDtU