Thanks for the link, that's a good article - also interesting to see power-to-weight flipped round the other way. I think the last paragraph is the most important though as it puts it all in context, which actually reinforces Chapman's principles rather than contradicting them:
"Of course, this is also if we only take into consideration the acceleration effects of weight and power. In road racing or in a daily driver, weight loss is more useful than in drag racing. Of course, regardless of our goals, the least amount of weight necessary is best."
Weight reduction means you shed speed more quickly when braking (less mass to decelerate), increase cornering speed due to reduced load on the tyres and accelerate more quickly, this is the basis of Chapman's case for weight reduction being the most effective route to faster lap times and better all round performance. A lighter car will also wear out its components (tyres, brakes and even suspension) less quickly than a heavier one, if they are both driven at the same speed.
If using less fuel is important to you that is another benefit, although if that is a high priority you are probably not in the market for an Emira or anything similar!