I watched psyshack's Okie FAS vids on CleanMPG this morning:
In the second one, he comments that his old Accord would coast a lot longer (about a mile) than his Civic in the video (5/8-3/4 mile). My guess is that this is because the Accord adds more weight than it does wind drag when compared to the Civic.
Glide times where speed normally decreases on a flat or slight downhill should increase as the car's weight is increased, all other things being equal. The amount of kinetic energy the car has is proportional to weight, and the rate at which speed is lost on flat land is a function of weight, aerodynamic drag and rolling friction -- increasing weight, lowering drag and lowering friction will all increase glide times.
The benefit of an increased glide time could be used two different ways: the engine could be ignited less frequently for the same speed range (fewer big pushes of gas at startup with an automatic, or fewer clutch slips for bump-starting a standard shift), or the speed range could be lowered (less variation in speed) for the same length of glide. The former would benefit fuel economy, the latter social acceptability. Either would be a plus.
Increasing weight would also dampen acceleration as well, which should also benefit fuel efficiency in cars with a high power/weight ratio (ie. cars for the American market) because a wider throttle position could be used to obtain the same rate of acceleration, and short of WOT, a wider throttle position generally yields a better engine efficiency.
Climbing ability during a glide should not be adversely affected; the energy lost during an ascent (U=mgh) is proportional to mass, but so is the kinetic energy of the car (E=1/2mv^2), so these should cancel each other. An ascent under engine power would require more throttle, but again, this should yield a greater engine efficiency and a longer glide on the descent.
Additional weight would also lower the aerodynamic profile in cars without ride height compensation. In general, lowering the front and raising the rear has generally been found to positively benefit fuel economy, so any weight added should be as forward in the car as possible. Probably the easiest would be steel weights or water jugs in the passenger seating areas, placed as far forward as practical.
A few caveats:
All other variables being equal, increasing weight would normally increase rolling friction. This is because the tires are deflected more with the increased weight, and tires constitute the main component of rolling friction.
The easy way around this would be to inflate the tires to compensate for the additional weight. If the height of each tire at its contact patch is precisely measured prior to adding weight (e.g. ground to the lowest point of the rim), then the tire could be inflated to achieve the same height after loading of the weight to compensate. This should yield very little net loss in rolling friction.
Also, this would mainly benefit commutes with long stretches of relatively flat (not mountainous) highway and few stops. If you normally brake much during your commute for stops or downhills, all the extra kinetic energy goes up in smoke (literally) and you end up with a net loss.
This would favor using water instead of steel -- if you find yourself stuck in traffic, you could just coast to a stop and dump the water for a more agile vehicle.
In hillier terrain, the speed variation would be greater because rate of descent increases with increased mass and decreased aerodynamic drag and rolling friction. So, if the car normally accelerates on a downhill, with more weight it will have a greater velocity at the bottom of the hill than it would otherwise. Depending on the grade, only so much can be done to compensate for this efficiently.
Unfortunately, I can't exploit this possibility for my particular commute because it's very hilly with a number of stops.
I'm drawing from these concepts from my time on the bike. Heavy riders (who can generate more power for their drag) and aerodynamic bicycles (e.g. faired recumbents) are generally faster on flat country roads, but the lighter diamond-frame bikes and riders are faster in hilly terrain and city traffic (because they effectively lose less energy to downhill wind drag and braking), and on bikes speed is generally an efficiency game.
I understand that this flies in the face of the general recommendation to remove any excess weight, which certainly benefits the majority of drivers with normal driving patterns.