We use a similar concept in rocketry to determine the optimum weight to achive maximum altitude... often, adding weight will increase the final altitude. However, I think the system is different enoguh from automobile FE that it is difficult to draw any conclusions. For one, there is only one pulse and one glide on a rocket, rather than a repeating cycle.
I guess the takeaway is that there is no hard and fast rule about weight. In general, lighter will be better... however, there may be cicumstances under which you may benefit from an increase in weight. My thought is that these conditions will be highly specific, difficult to indentify, and unlikely to be extrapolated to "general use."
A contest may be an area where enough of the variables are known that you can make some improvements, but daily driving is such a crapshoot that it'd be a heroic effort. Not that that should stop us from trying.
(Random thoughts... would a lighter bullet undergo increased acceleration from the same amount of propellant, therefore exiting the barrel more quickly and experiencing less total force than a heavier bullet? Thus, a lighter bullet may actually have less total energy for a given propellant mass and barrel length than a heavier bullet. As can't think of a corrolary of this with respect to cars, the bullet analogy might not work.)