bleaching it is part of the refining process, so it's high on the industrial waste scale, and some of that is still in it when it hits the table, which adds to your chlorine uptake. (free radicals - or oxidants if you're into that)
the other big thing is that white sugar is a type of sugar that enters your blood stream instantly - as opposed to "natural sugars' like fructose which have to be broken down into glucose and so do not cause the sugar spike/insulin cycle becuase they enter your blood at a slower rate. (sort of like the difference between getting 1" of rain in 20 minutes versus a steady soaker that takes 8 hours to dump the same amount on your lawn) This sugar spike/insulin spike cycle is thought to be one of the major causes of type II diabetes as well as some forms of pancreatitis.
Because of the refining process and the way it's absorbed into your blood, there's also a theory that white sugar changes your body's pH which can leave you more succeptible to some illnesses and infections. (people used to pack food in sugar or honey to preserve it in places where the didn't have access to a lot of salt)
There's plenty of other information out there on the ills of refined white food (rice and flour, too - which is part of the push for whole wheat/brown rice over the past 30 years) that i don't have at my fingertips right now - some of which makes sense, some of which is akin to religion in that if you don't want to believe, their "proofs" won't convince you.