It's those chemicals that are responsible for the taste of tea. Here is the breakdown:
Exactly how much remains throughout multiple infusions really depends on the individual tea. The link above should give you some idea, however.
I wouldn't particularly depend on tea as a weight-loss potion, however. I think the most it will do is give you an extra pound or two loss when you eat right and exercise. You may already know this, and I mean no offense, but some people do tend to hold unrealistic expectations of tea when it comes to weight loss.