... During all this time, the heavier boat had have an equal or a higher speed than the lighter one, and hence traveled a longer distance.
It is logic that a boat has to accelerate after each de-accelertaion. Hence from start to finish we have n de-accelertions and n+1 (the +1 is at the start of the race) accelerations. So the hevaier boat makes n times something good and looses only one time something.

The critical issue (and one that effects catamarans as well as any other sailboat) is that the total weight essentially contributes to both drag and power. The trick is to maximise the power-to-weight(drag) ratio ...